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.

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

Alois P. Heinz, Table of n, a(n) for n = 0..250

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

Adjacent sequences: A261958 A261959 A261960 * A261962 A261963 A261964

Keyword

nonn

Author

Alois P. Heinz, Sep 06 2015

Status

approved