A115276 Number of partitions of {1,...,n} into block sizes not a multiple of 4.

1, 1, 2, 5, 14, 47, 173, 702, 3124, 14901, 76405, 417210, 2411466, 14731095, 94573911, 636575050, 4480990936, 32887804361, 251236573561, 1993395483746, 16397468177406, 139634290253907, 1229013163330947, 11166172488138322, 104593176077399652

Offset: 0

Author

Christian G. Bower, Jan 18 2006

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A001935, A003724, A115275, A115277.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
      irem(j, 4)=0, 0, binomial(n-1, j-1)*a(n-j)), j=1..n))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 17 2015

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[If[Mod[j, 4] == 0, 0, Binomial[n - 1, j - 1]*a[n - j]], {j, 1, n}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 20 2016, after Alois P. Heinz *)

Formula

E.g.f.: exp(sinh(x)+(cosh(x)-cos(x))/2).