|
Search: id:A113107
|
|
|
| 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<i<n. |
|
+0
14
|
|
| 1, 1, 5, 85, 4985, 1082905, 930005021, 3306859233805, 50220281721033905, 3328966349792343354865, 978820270264589718999911669, 1292724512951963810375572954693765
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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 5-th power.
|
|
LINKS
|
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.
|
|
PROGRAM
|
(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: A101928 A012788 A012815 this_sequence A018925 A140159 A073862
Adjacent sequences: A113104 A113105 A113106 this_sequence A113108 A113109 A113110
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005
|
|
|
Search completed in 0.002 seconds
|
