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

%I A271207 #12 May 27 2018 07:00:45
%S A271207 1,1,2,4,10,28,89,315,1233,5285,24583,123062,658335,3741625,22483415,
%T A271207 142264589,944652336,6562959239,47583055191,359196368057,
%U A271207 2817394708454,22919157785777,193045807856919,1681025045594032,15112573721911697,140088106892677440
%N A271207 Number of set partitions of [n] avoiding triples (t,t+1,t+2) having t+i in block b+i for some b.
%H A271207 Alois P. Heinz, <a href="/A271207/b271207.txt">Table of n, a(n) for n = 0..300</a>
%H A271207 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A271207 a(4) = 10: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 13|2|4, 14|23, 1|234, 1|23|4.
%p A271207 b:= proc(n, i, t, m) option remember; `if`(n=0, 1, add(`if`(
%p A271207      t and j=i+1, 0, b(n-1, j, is(j=i+1), max(m, j))), j=1..m+1))
%p A271207     end:
%p A271207 a:= n-> b(n, 1, false, 0):
%p A271207 seq(a(n), n=0..30);
%t A271207 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}]];
%t A271207 a[n_] := b[n, 1, False, 0];
%t A271207 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A271207 Column k=0 of A271206.
%K A271207 nonn
%O A271207 0,3
%A A271207 _Alois P. Heinz_, Apr 01 2016