A274841 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of eight.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 38, 73, 136, 247, 438, 757, 1268, 3303, 7883, 17801, 38745, 82179, 170907, 349341, 700517, 2066512, 5768089, 15386070, 39563059, 98692628, 239843745, 569063602, 1318211431, 4290275275, 13443268926

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..902

Wikipedia, Partition of a set

Example

a(8) = 1: 1|2|3|4|5|6|7|8.
a(9) = 2: 19|2|3|4|5|6|7|8, 1|2|3|4|5|6|7|8|9.
a(10) = 3: 19|2(10)|3|4|5|6|7|8, 1|2(10)|3|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).

Maple

b:= proc(n, m, t) option remember; `if`(n=0, 1,
     add(`if`(irem(j-t, 8)=0, b(n-1, max(m, j),
              irem(t+1, 8)), 0), j=1..m+1))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..45);

Mathematica

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 8] == 0, b[n - 1, Max[m, j], Mod[t + 1, 8]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=8 of A274835.

Sequence in context: A051885 A227378 A226637 * A247227 A048410 A341161

Adjacent sequences: A274838 A274839 A274840 * A274842 A274843 A274844

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved