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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.
2
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
0,3
LINKS
EXAMPLE
a(4) = 10: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 13|2|4, 14|23, 1|234, 1|23|4.
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 *)
CROSSREFS
Column k=0 of A271206.
Sequence in context: A149832 A229046 A363110 * A091175 A090594 A361912
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 01 2016
STATUS
approved