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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
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];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 24 2018, translated from Maple *)
CROSSREFS
Column k=2 of A261959.
Cf. A261962.
Sequence in context: A272433 A272432 A272431 * A177030 A189974 A316184
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 06 2015
STATUS
approved