%I #13 May 29 2018 08:27:22
%S 1,1,2,3,5,7,10,14,19,26,34,45,58,75,95,121,151,189,234,289,354,433,
%T 526,637,768,923,1105,1319,1569,1861,2202,2597,3056,3587,4201,4908,
%U 5723,6658,7732,8961,10367,11971,13802,15884,18253,20942,23992,27445,31353
%N Number of partitions of n with at most two even parts.
%C Also number of partitions of n+4 with exactly two even parts. Example: a(3)=3 because the partitions of 7 with exactly two even parts are [4,2,1], [3,2,2] and [2,2,1,1,1]. a(n)=A116482(n+4,2). - _Emeric Deutsch_, Feb 21 2006
%D Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70, Eq. 2, with k=2. - _N. J. A. Sloane_, Aug 31 2014
%F G.f.: (1/((1-x^2)*(1-x^4)))/Product(1-x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n with at most k even parts is (1/Product(1-x^(2*i), i=1..k))/Product(1-x^(2*i+1), i=0..infinity).
%F a(n) ~ 3^(3/4) * n^(1/4) * exp(Pi*sqrt(n/3)) / (8*Pi^2). - _Vaclav Kotesovec_, May 29 2018
%e a(3)=3 because we have [3],[2,1] and [1,1,1].
%t CoefficientList[ Series[(1/((1 - x^2)*(1 - x^4)))/Product[1 - x^(2i + 1), {i, 0, 50}], {x, 0, 48}], x] (* _Robert G. Wilson v_, Aug 16 2004 *)
%Y Cf. A038348.
%Y Cf. A116482.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Aug 16 2004
%E More terms from _Robert G. Wilson v_, Aug 17 2004
%E More terms from _Emeric Deutsch_, Feb 21 2006