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 A113079 Number of tournament sequences: a(n) gives the number of n-th generation descendents of a node labeled (5) in the tree of tournament sequences. 11
 1, 5, 40, 515, 10810, 376175, 22099885, 2231417165, 393643922005, 123097221805100, 69087264010363930, 70321483026073531730, 130954011392485408662370, 449450774746306949114288795 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals column 5 of square table A093729. Also equals column 0 of the matrix 5th power of triangle A097710, which satisfies the matrix recurrence: A097710(n,k) = [A097710^2](n-1,k-1) + [A097710^2](n-1,k) for n>k>=0. LINKS Table of n, a(n) for n=0..13. M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44. EXAMPLE The tree of tournament sequences of descendents of a node labeled (5) begins: [5]; generation 1: 5->[6,7,8,9,10]; generation 2: 6->[7,8,9,10,11,12], 7->[8,9,10,11,12,13,14], 8->[9,10,11,12,13,14,15,16], 9->[10,11,12,13,14,15,16,17,18], 10->[11,12,13,14,15,16,17,18,19,20]; ... 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, q=2)=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^q)[r-1, c-1])+(M^q)[r-1, c]))); return((M^5)[n+1, 1])} CROSSREFS Cf. A113077, A113078, A008934, A113089, A113096, A113098, A113100, A113107, A113109, A113111, A113113. Sequence in context: A088695 A365779 A145166 * A211046 A138427 A277405 Adjacent sequences: A113076 A113077 A113078 * A113080 A113081 A113082 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 14 2005 STATUS approved

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