A274838 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of five.

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 13, 26, 49, 88, 151, 397, 951, 2145, 4633, 9643, 28898, 80843, 214126, 542081, 1317924, 4392295, 13871122, 41984457, 122463762, 344409561, 1273659431, 4463980333, 14994032599, 48610148069, 152506484015, 614168698264

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..808

Wikipedia, Partition of a set

Example

a(7) = 3: 16|27|3|4|5, 1|27|3|4|5|6, 1|2|3|4|5|6|7.
a(8) = 4: 16|27|38|4|5, 1|27|38|4|5|6, 1|2|38|4|5|6|7, 1|2|3|4|5|6|7|8.
a(9) = 5: 16|27|38|49|5, 1|27|38|49|5|6, 1|2|38|49|5|6|7, 1|2|3|49|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, 5)=0, b(n-1, max(m, j),
              irem(t+1, 5)), 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, 5] == 0, b[n - 1, Max[m, j], Mod[t + 1, 5]], 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=5 of A274835.

Sequence in context: A121433 A317778 A259541 * A200331 A010349 A032995

Adjacent sequences: A274835 A274836 A274837 * A274839 A274840 A274841

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved