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A274838 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of five. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified June 24 22:23 EDT 2019. Contains 324337 sequences. (Running on oeis4.)