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 A113100 Number of 4-tournament sequences: a(n) gives the number of increasing sequences of n positive integers (t_1,t_2,...,t_n) such that t_1 = 3 and t_i = 3 (mod 3) and t_{i+1} <= 4*t_i for 1
 1, 3, 27, 693, 52812, 12628008, 9924266772, 26507035453923, 246323730279500082, 8100479557816637139288, 954983717308947379891713642, 407790020849346203244152231395953 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Column 0 of triangle A113099; A113099 is the matrix cube of triangle A113095, which satisfies the matrix recurrence: A113095(n,k) = [A113095^4](n-1,k-1) + [A113095^4](n-1,k). Also equals column 3 of square table A113092. LINKS T. D. Noe, Table of n, a(n) for n=0..30 M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44. EXAMPLE The tree of 4-tournament sequences of descendents of a node labeled (3) begins: ; generation 1: 3->[6,9,12]; generation 2: 6->[9,12,15,18,21,24], 9->[12,15,18,21,24,27,30,33,36], 12->[15,18,21,24,27,30,33,36,39,42,45,48]; ... Then a(n) gives the number of nodes in generation n. Also, a(n+1) = sum of labels of nodes in generation n. PROG (PARI) {a(n)=local(M=matrix(n+1, n+1)); for(r=1, n+1, for(c=1, r, M[r, c]=if(r==c, 1, if(c>1, (M^4)[r-1, c-1])+(M^4)[r-1, c]))); return((M^3)[n+1, 1])} CROSSREFS Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113107, A113109, A113111, A113113. Sequence in context: A185237 A099084 A085656 * A038379 A047656 A193610 Adjacent sequences:  A113097 A113098 A113099 * A113101 A113102 A113103 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 14 2005 STATUS approved

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)