Formerly M N 0, 1, 2, 5, 12, 29, 70,,,, list ; graph ; refs ; listen ; history ; text ; internal format OFFSET 0,3 COMMENTS Sometimes also called lambda numbers. S n,xChebyshev's polynomials of the first,resp. See Aresp. Sequence contains the denominators. See A for definition of Pisot sequences.
Wilson Sums of antidiagonals of A [Pascal's triangle squared]. The odd composite numbers which are Pell pseudoprimes i. End Equals row sums of triangle A starting with offset 1. AdamsonFeb 21 Equals eigensequence of triangle A AdamsonFeb 12 Another combinatorial interpretation of a n-1 arises from a simple tiling scenario. Namely, a n-1 gives the number of ways of tiling a 1 X n rectangle with indistinguishable 1 X 2 rectangles and 1 X 1 squares that come in two varieties, say, A and B.
BuddenhagenAug 14 An elephant sequence, see A For the corner squares six A vectors, with decimal values between 21 andlead to this sequence without the leading 0. For the central square these vectors lead to the companion sequence A Such a circle has coordinates equal to its radius. Let C 0 be the t-circle with radius 1. See similar Comments for A and ASep 14 Two flaps can be lowered over the same square in 2 ways, depending on which one is on top.
The n-th Pell number counts the ways n-1 flaps can be lowered. MoralesSep 18 Define a -n to be a n for n odd and -a n for n even. This formula generalizes the formula used to define this sequence. Contrast with entry from Bob Selcoe dated Jun 21 DevilletSep 28 Also the number of matchings in the n-1 -centipede graph.
SimayMay 25 1, 2, 5, 12, 29, Beiler, Recreations in the Theory of Numbers. New York: Dover, pp. Belcastro, Tilings of 2 x n Grids on Surfaces, preprint. Borwein, D. Bailey and R. See p. Finch, Mathematical Constants, Cambridge,Section 1. Shaun Giberson and Thomas J. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, Springer-Verlag, NY, 2nd ed. Roberts, Lure of the Integers, Math. America,p. Manfred R. Schroeder, "Number Theory in Science and Communication", 5th ed.Martinez IINov 05 a n is the number of subdiagonal paths from 0, 0 to n, n consisting of steps East 1, 0North 0, 1 and Northeast 1, 1 sometimes called royal paths.
A diagonal is a straight line joining two nonconsecutive vertices and dissection means the diagonals are noncrossing though they may share an endpoint.
AdamsonSep 12 a n is also the number of order-preserving and order-decreasing partial transformations of an n-chain. This sequence is the rightmost diagonal. HawkesFeb 15 a n is the number of unary-rooted size n unary-binary trees each node has either 1 or 2 degree out. The number of general n X n matrices of weight n which percolate is given in A The permutations are precisely the permutations that are sortable by a decreasing stack followed by an increasing stack in series.
Aigner, Enumeration via ballot numbers, Discrete Math. Andrica and E. Ionascu, On the number of polynomials with coefficients in [n], An. Ovidius Constanta,to appear. Barcucci, E. Discrete Math.
P Barry, Riordan arrays, generalized Narayana triangles, and series reversion, Linear Algebra and its Applications, Bodini, A. Genitrini, F. Peschanski and N. Brlek, E. Duchi, E. Pergola and S. Rinaldi, On the equivalence problem for succession rules, Discr. William Y. Chen and Carol J. Comtet, Advanced Combinatorics, Reidel,p. Davenport, L.
Shapiro and L. Deng, Eva Y. See p. Deutsch, A bijective proof of an equation linking the Schroeder numbers, large and small, Discrete Math. Domb and A. Barrett, Enumeration of ladder graphs, Discrete Math.In order to demonstrate some of the ways in which people have found the OEIS useful, we have assembled a list of papers and books that reference it. The list has been broken into subsections according to the first few letters of the first author's last name. The main reason for doing this is to update the OEIS entries with information about recent work on the sequences.
By referring people to this list we can say that over 8, works have found it helpful, and that many of these works say things like "This discovery was made with the help of the OEIS". If you have found the OEIS useful in your own work, and wish to reference it, the usual citation is. But both of these special formats take time, so normally I don't use them, because I have about of these articles to process, with more arriving every few days.
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Journal of integer sequences
You already recently rated this item. Your rating has been recorded.A tree is an ordered tree in which every vertex has at most two children.
Ties are counted even when candidates A and B lose the election. NoeMar 16 Row sums of triangle A Weisstein, Mar 14 It has apparently not been proved that no [other] prime central trinomials exist.
See the papers by Ekhad-Zeilberger and Zeilberger. A and B are disjoint and ii. A and B contain the same number of elements. Barcucci, R. Pinzani, R. Sprugnoli, The Motzkin family, P. A, Vol. Comtet, Advanced Combinatorics, Reidel,pp. Teubner, Leipzig,Series 1Vol. Graham, D. Knuth and O. Patashnik, Concrete Mathematics.
Addison-Wesley, Reading, MA,p. Henrici, Applied and Computational Complex Analysis. Wiley, NY, 3 vols. Riordan, Combinatorial Identities, Wiley,p. Stanley, Enumerative Combinatorics, Cambridge, Vol. Lin Yang and S. Yang, The parametric Pascal rhombus. See p. Noe G.In mathematicsan integer sequence is a sequence i. An integer sequence may be specified explicitly by giving a formula for its n th term, or implicitly by giving a relationship between its terms.
For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, The sequence 0, 3, 8, 15, Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect numbereven though we do not have a formula for the n th perfect number. The set of computable integer sequences is countable.
The set of all integer sequences is uncountable with cardinality equal to that of the continuumand so not all integer sequences are computable. Although some integer sequences have definitions, there is no systematic way to define what it means for an integer sequence to be definable in the universe or in any absolute model independent sense.
Suppose the set M is a transitive model of ZFC set theory. The transitivity of M implies that the integers and integer sequences inside M are actually integers and sequences of integers. An integer sequence is a definable sequence relative to M if there exists some formula P x in the language of set theory, with one free variable and no parameters, which is true in M for that integer sequence and false in M for all other integer sequences. In each such Mthere are definable integer sequences that are not computable, such as sequences that encode the Turing jumps of computable sets.
For some transitive models M of ZFC, every sequence of integers in M is definable relative to M ; for others, only some integer sequences are Hamkins et al.
There is no systematic way to define in M itself the set of sequences definable relative to M and that set may not even exist in some such M. Similarly, the map from the set of formulas that define integer sequences in M to the integer sequences they define is not definable in M and may not exist in M.
However, in any model that does possess such a definability map, some integer sequences in the model will not be definable relative to the model Hamkins et al. If M contains all integer sequences, then the set of integer sequences definable in M will exist in M and be countable and countable in M. A sequence of positive integers is called a complete sequence if every positive integer can be expressed as a sum of values in the sequence, using each value at most once. From Wikipedia, the free encyclopedia.
Sequences and series. Cauchy sequence Monotone sequence Periodic sequence. Convergent series Divergent series Conditional convergence Absolute convergence Uniform convergence Alternating series Telescoping series.
Riemann zeta function. Generalized hypergeometric series Hypergeometric function of a matrix argument Lauricella hypergeometric series Modular hypergeometric series Riemann's differential equation Theta hypergeometric series. Book Category. Categories : Integer sequences Arithmetic functions. Hidden categories: Commons category link is on Wikidata.
Namespaces Article Talk. Views Read Edit View history. Help Community portal Recent changes Upload file. Download as PDF Printable version. Wikimedia Commons. Wikimedia Commons has media related to Integer sequences.The Journal of Integer Sequences is a peer-reviewed open-access academic journal in mathematics, specializing in research papers about integer sequences.
It was founded in by Neil Sloane.
Journal of integer sequences
Needing an outlet for research papers concerning the sequences he was collecting in OEIS, he founded the journal. There are no page charges for authors, and all papers are free to all readers. The journal publishes approximately 50—75 papers annually. In most years from toSCImago Journal Rank has ranked the Journal of Integer Sequences as a third-quartile journal in discrete mathematics and combinatorics.
Works Citing OEIS
From Wikipedia, the free encyclopedia. Academic journal. University of Waterloo. Open access. Categories : Integer sequences Mathematics journals Open access journals Publications established in English-language journals Irregular journals. Hidden categories: All articles with dead external links Articles with dead external links from December Articles with permanently dead external links Articles with short description Irregular journals infobox.
Namespaces Article Talk. Views Read Edit View history. Help Community portal Recent changes Upload file. Download as PDF Printable version. Integer sequences. Jeffrey Shallit. Journal homepage Online access.