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A274837 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of four. 2
1, 1, 1, 1, 1, 2, 3, 4, 5, 11, 22, 41, 72, 191, 459, 1033, 2209, 6696, 18777, 49526, 124011, 419203, 1329966, 4009931, 11544970, 43203329, 152247581, 511143253, 1644388769, 6707557342, 25952578959, 95992345048, 340793163873, 1501194339387, 6305017609678 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..768

Wikipedia, Partition of a set

EXAMPLE

a(7) = 4: 15|26|37|4, 1|26|37|4|5, 1|2|37|4|5|6, 1|2|3|4|5|6|7.

a(8) = 5: 15|26|37|48, 1|26|37|48|5, 1|2|37|48|5|6, 1|2|3|48|5|6|7, 1|2|3|4|5|6|7|8.

a(9) = 11: 159|26|37|48, 15|26|37|48|9, 19|26|37|48|5, 1|26|37|48|59, 19|2|37|48|5|6, 1|2|37|48|59|6, 19|2|3|48|5|6|7, 1|2|3|48|59|6|7, 19|2|3|4|5|6|7|8, 1|2|3|4|59|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, 4)=0, b(n-1, max(m, j),

              irem(t+1, 4)), 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, 4] == 0, b[n - 1, Max[m, j], Mod[t + 1, 4]], 0], {j, 1, m + 1}]];

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

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A274835.

Sequence in context: A118597 A083160 A123823 * A064959 A217650 A032988

Adjacent sequences:  A274834 A274835 A274836 * A274838 A274839 A274840

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 08 2016

STATUS

approved

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)