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 A113107 Number of 5-tournament sequences: a(n) gives the number of increasing sequences of n positive integers (t_1,t_2,...,t_n) such that t_1 = 1 and t_i = 1 (mod 4) and t_{i+1} <= 5*t_i for 1
 1, 1, 5, 85, 4985, 1082905, 930005021, 3306859233805, 50220281721033905, 3328966349792343354865, 978820270264589718999911669, 1292724512951963810375572954693765 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals column 0 of triangle A113106 which satisfies recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k), where A113106^5 is the matrix 5th power. LINKS Table of n, a(n) for n=0..11. M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44. EXAMPLE The tree of 5-tournament sequences of descendents of a node labeled (1) begins: [1]; generation 1: 1->[5]; generation 2: 5->[9,13,17,21,25]; ... 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^5)[r-1, c-1])+(M^5)[r-1, c]))); return(M[n+1, 1])} CROSSREFS Cf. A008934, A113077, A113078, A113079, A113085, A113089, A113096, A113098, A113100, A113109, A113111, A113113. Sequence in context: A208886 A192055 A012815 * A317355 A018925 A309327 Adjacent sequences: A113104 A113105 A113106 * A113108 A113109 A113110 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 14 2005 STATUS approved

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Last modified March 4 10:33 EST 2024. Contains 370528 sequences. (Running on oeis4.)