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A171966 Number of partitions of n having no more odd than even parts.

%I A171966 #15 Aug 19 2021 20:04:37
%S A171966 1,0,1,1,2,3,4,6,8,12,15,21,28,37,49,63,83,105,138,171,223,275,353,
%T A171966 433,551,673,846,1031,1282,1558,1922,2327,2848,3440,4179,5032,6078,
%U A171966 7293,8763,10482,12534,14943,17797,21146,25090,29719,35138,41493,48908,57578
%N A171966 Number of partitions of n having no more odd than even parts.
%C A171966 a(n) = A108949(n) + A045931(n) = A000041(n) - A108950(n).
%C A171966 a(n) = Sum_{k=-floor(n/2)+(n mod 2)..0} A240009(n,k). - _Alois P. Heinz_, Mar 30 2014
%H A171966 Alois P. Heinz, <a href="/A171966/b171966.txt">Table of n, a(n) for n = 0..1000</a>
%p A171966 b:= proc(n, i, t) option remember; `if`(n=0,
%p A171966       `if`(t<=0, 1, 0), `if`(i<1, 0, b(n, i-1, t)+
%p A171966       `if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1)))))
%p A171966     end:
%p A171966 a:= n-> b(n$2, 0):
%p A171966 seq(a(n), n=0..80);  # _Alois P. Heinz_, Mar 30 2014
%t A171966 $RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t <= 0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t+(2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Jun 30 2015, after _Alois P. Heinz_ *)
%Y A171966 Cf. A130780, A171967, A240009.
%K A171966 nonn
%O A171966 0,5
%A A171966 _Reinhard Zumkeller_, Jan 21 2010