A271207 Number of set partitions of [n] avoiding triples (t,t+1,t+2) having t+i in block b+i for some b.

1, 1, 2, 4, 10, 28, 89, 315, 1233, 5285, 24583, 123062, 658335, 3741625, 22483415, 142264589, 944652336, 6562959239, 47583055191, 359196368057, 2817394708454, 22919157785777, 193045807856919, 1681025045594032, 15112573721911697, 140088106892677440

Offset: 0

Author

Alois P. Heinz, Apr 01 2016

Keywords

• nonn

Examples

			a(4) = 10: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 13|2|4, 14|23, 1|234, 1|23|4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Wikipedia, Partition of a set

Crossrefs

Column k=0 of A271206.

Programs

Maple

b:= proc(n, i, t, m) option remember; `if`(n=0, 1, add(`if`(
     t and j=i+1, 0, b(n-1, j, is(j=i+1), max(m, j))), j=1..m+1))
    end:
a:= n-> b(n, 1, false, 0):
seq(a(n), n=0..30);

Mathematica

b[n_, i_, t_, m_] := b[n, i, t, m] = If[n == 0, 1, Sum[If[t && j == i + 1, 0, b[n - 1, j, j == i + 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := b[n, 1, False, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)