A274839 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of six.

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 15, 30, 57, 104, 183, 310, 811, 1939, 4377, 9497, 19987, 40883, 121620, 339817, 902822, 2301883, 5665060, 13489425, 44503335, 140080438, 425111779, 1250942834, 3575716011, 9910354002, 36376567529, 127026151621

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..842

Wikipedia, Partition of a set

Example

a(7) = 2: 17|2|3|4|5|6, 1|2|3|4|5|6|7.
a(8) = 3: 17|28|3|4|5|6, 1|28|3|4|5|6|7, 1|2|3|4|5|6|7|8.
a(9) = 4: 17|28|39|4|5|6, 1|28|39|4|5|6|7, 1|2|39|4|5|6|7|8, 1|2|3|4|5|6|7|8|9.

Maple

b:= proc(n, m, t) option remember; `if`(n=0, 1,
     add(`if`(irem(j-t, 6)=0, b(n-1, max(m, j),
              irem(t+1, 6)), 0), j=1..m+1))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..40);

Mathematica

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 6] == 0, b[n - 1, Max[m, j], Mod[t + 1, 6]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A274835.

Sequence in context: A263469 A165804 A055402 * A361809 A367933 A356194

Adjacent sequences: A274836 A274837 A274838 * A274840 A274841 A274842

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved