A274836 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of three.

1, 1, 1, 1, 2, 3, 4, 9, 18, 33, 89, 215, 481, 1486, 4187, 10974, 37907, 121114, 362953, 1385575, 4924557, 16494655, 68685792, 268113185, 990074770, 4455129525, 18896355932, 76116156873, 367577989487, 1679905933299, 7313571105815, 37669220146964

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..721

Wikipedia, Partition of a set

Example

a(5) = 3: 14|25|3, 1|25|3|4, 1|2|3|4|5.
a(6) = 4: 14|25|36, 1|25|36|4, 1|2|36|4|5, 1|2|3|4|5|6.
a(7) = 9: 147|25|36, 14|25|36|7, 17|25|36|4, 1|25|36|47, 17|2|36|4|5, 1|2|36|47|5, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.

Maple

b:= proc(n, m, t) option remember; `if`(n=0, 1,
     add(`if`(irem(j-t, 3)=0, b(n-1, max(m, j),
              irem(t+1, 3)), 0), j=1..m+1))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..35);

Mathematica

b[n_, m_, t_] := b[n, m, t] = If[n == 0, 1, Sum[If[Mod[j-t, 3] == 0, b[n-1, Max[m, j], Mod[t+1, 3]], 0], {j, 1, m+1}]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)

Crossrefs

Column k=3 of A274835.

Sequence in context: A338585 A145027 A088275 * A322783 A014281 A220364

Adjacent sequences: A274833 A274834 A274835 * A274837 A274838 A274839

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2016

Status

approved