Neuwirth, Erich Computing tournament sequence numbers efficiently with matrix techniques. (English) Zbl 1021.05004 Sémin. Lothar. Comb. 47, 12 p. (2002). Summary: We give a new, “almost explicit” formula for tournament numbers, representing them as upper left elements of the \(n\)th power of a matrix with an explicit formula for elements of the original matrix. Using this representation, we show how to compute tournament numbers in time complexity \(O(n^6)\). Cited in 1 Document MSC: 05A15 Exact enumeration problems, generating functions 15A24 Matrix equations and identities 11B83 Special sequences and polynomials 05A16 Asymptotic enumeration Keywords:tournament matrix; number of tournament sequences; tournament numbers PDFBibTeX XMLCite \textit{E. Neuwirth}, Sémin. Lothar. Comb. 47, 12 p. (2002; Zbl 1021.05004) Full Text: EuDML Online Encyclopedia of Integer Sequences: Number of tournament sequences: sequences (a_1, a_2, ..., a_n) with a_1 = 1 such that a_i < a_{i+1} <= 2*a_i for all i.