A274842 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of nine.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 42, 81, 152, 279, 502, 885, 1524, 2547, 6629, 15815, 35713, 77769, 165155, 344379, 707693, 1434461, 2859871, 8415994, 23485835, 62727630, 161710529, 404995340, 989816263, 2367377650, 5547588797

Offset

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..928

Wikipedia, Partition of a set

Example

a(9) = 1: 1|2|3|4|5|6|7|8|9.
a(10) = 2: 1(10)|2|3|4|5|6|7|8|9, 1|2|3|4|5|6|7|8|9|(10).
a(11) = 3: 1(10)|2(11)|3|4|5|6|7|8|9, 1|2(11)|3|4|5|6|7|8|9|(10), 1|2|3|4|5|6|7|8|9|(10)|(11).

Maple

b:= proc(n, m, t) option remember; `if`(n=0, 1,
     add(`if`(irem(j-t, 9)=0, b(n-1, max(m, j),
              irem(t+1, 9)), 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, 9] == 0, b[n - 1, Max[m, j], Mod[t + 1, 9]], 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=9 of A274835.

Sequence in context: A061511 A138142 A085890 * A134817 A067581 A099469

Adjacent sequences: A274839 A274840 A274841 * A274843 A274844 A274845

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved