%I #18 May 15 2023 11:13:51

%S 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,9,11,13,16,18,22,

%T 25,30,35,41,47,56,64,76,87,102,117,137,157,183,210,243,278,323,368,

%U 425,485,558,636,730,830,951,1081,1235,1401,1598,1810,2060

%N Number of partitions of n into an even number of parts, the least being 5; also, a(n+5) = number of partitions of n into an odd number of parts, each >=5.

%H Alois P. Heinz, <a href="/A027197/b027197.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) + A027191(n) = A026798(n). - _R. J. Mathar_, Oct 18 2019

%F G.f.: x^10 * Sum_{k>=0} x^(10*k)/Product_{j=1..2*k+1} (1-x^j). - _Seiichi Manyama_, May 15 2023

%p b:= proc(n, i, t) option remember; `if`(n=0, t,

%p `if`(i>n, 0, b(n, i+1, t)+b(n-i, i, 1-t)))

%p end:

%p a:= n-> `if`(n<5, 0, b(n-5, 5, 0)):

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 18 2019

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i > n, 0, b[n, i + 1, t] + b[n - i, i, 1 - t]]];

%t a[n_] := If[n < 5, 0, b[n - 5, 5, 0]];

%t a /@ Range[100] (* _Jean-François Alcover_, Feb 06 2020, after _Alois P. Heinz_ *)

%Y Cf. A026798, A027191.

%K nonn

%O 1,20

%A _Clark Kimberling_