|
|
A261961
|
|
Number of ordered set partitions of {1,2,...,n} such that no part has the same size as any of its two immediate predecessors.
|
|
3
|
|
|
1, 1, 1, 7, 9, 31, 403, 1597, 7913, 68551, 539691, 4359037, 48419715, 560648557, 4985097601, 59798395027, 869794249513, 11143895125527, 159575614945315, 2593765421983597, 38615447492264219, 642012651525487501, 11768461266053785921, 220201814964135821967
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
MAPLE
|
b:= proc(n, i, j) option remember; `if`(n=0, 1, add(
`if`(k=i or k=j, 0, (t-> binomial(n, k)*b(t,
`if`(k>t, 0, k), `if`(i>t, 0, i)))(n-k)), k=1..n))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..30);
|
|
MATHEMATICA
|
b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, Sum[If[k == i || k == j, 0, Function[t, Binomial[n, k]*b[t, If[k > t, 0, k], If[i > t, 0, i]]][n - k]], {k, 1, n}]];
a[n_] := b[n, 0, 0];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|