A274843 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of ten.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 23, 46, 89, 168, 311, 566, 1013, 1780, 3059, 5106, 13283, 31683, 71545, 155833, 331139, 691387, 1424525, 2902605, 5848135, 11610871, 34108236, 95170569, 254432006, 657159051, 1650540916

Offset

0,12

Links

Alois P. Heinz, Table of n, a(n) for n = 0..953

Wikipedia, Partition of a set

Example

a(10) = 1: 1|2|3|4|5|6|7|8|9|(10).
a(11) = 2: 1(11)|2|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, 10)=0, b(n-1, max(m, j),
              irem(t+1, 10)), 0), j=1..m+1))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..50);

Mathematica

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j - t, 10] == 0, b[n - 1, Max[m, j], Mod[t + 1, 10]], 0], {j, 1, m + 1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=10 of A274835.

Sequence in context: A179309 A032946 A273738 * A039156 A132030 A288327

Adjacent sequences: A274840 A274841 A274842 * A274844 A274845 A274846

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved