|
%I #8 Jan 20 2016 08:22:14
%S 1,1,2,5,14,47,173,702,3124,14901,76405,417210,2411466,14731095,
%T 94573911,636575050,4480990936,32887804361,251236573561,1993395483746,
%U 16397468177406,139634290253907,1229013163330947,11166172488138322,104593176077399652
%N Number of partitions of {1,...,n} into block sizes not a multiple of 4.
%H Alois P. Heinz, <a href="/A115276/b115276.txt">Table of n, a(n) for n = 0..500</a>
%F E.g.f.: exp(sinh(x)+(cosh(x)-cos(x))/2).
%p a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
%p irem(j, 4)=0, 0, binomial(n-1, j-1)*a(n-j)), j=1..n))
%p end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 17 2015
%t 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_ *)
%Y Cf. A001935, A003724, A115275, A115277.
%K nonn
%O 0,3
%A _Christian G. Bower_, Jan 18 2006
|
