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A274839 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of six. 2
1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 15, 30, 57, 104, 183, 310, 811, 1939, 4377, 9497, 19987, 40883, 121620, 339817, 902822, 2301883, 5665060, 13489425, 44503335, 140080438, 425111779, 1250942834, 3575716011, 9910354002, 36376567529, 127026151621 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..842

Wikipedia, Partition of a set

EXAMPLE

a(7) = 2: 17|2|3|4|5|6, 1|2|3|4|5|6|7.

a(8) = 3: 17|28|3|4|5|6, 1|28|3|4|5|6|7, 1|2|3|4|5|6|7|8.

a(9) = 4: 17|28|39|4|5|6, 1|28|39|4|5|6|7, 1|2|39|4|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, 6)=0, b(n-1, max(m, j),

              irem(t+1, 6)), 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, 6] == 0, b[n - 1, Max[m, j], Mod[t + 1, 6]], 0], {j, 1, m + 1}]];

a[n_] := b[n, 0, 1];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=6 of A274835.

Sequence in context: A263469 A165804 A055402 * A065640 A264974 A308334

Adjacent sequences:  A274836 A274837 A274838 * A274840 A274841 A274842

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 08 2016

STATUS

approved

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Last modified August 21 23:00 EDT 2019. Contains 326169 sequences. (Running on oeis4.)