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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A001935, A003724, A115275, A115277.

Sequence in context: A149903 A149904 A287888 * A343664 A327702 A317784

Adjacent sequences: A115273 A115274 A115275 * A115277 A115278 A115279

Keyword

nonn

Author

Christian G. Bower, Jan 18 2006

Status

approved