A274837 Number of set partitions of [n] such that the difference between each element and its block index is a multiple of four.

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

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-François 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