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A132462 Number of partitions of n into distinct parts congruent to 0 or 2 modulo 3.

%I A132462 #23 Sep 23 2024 04:17:57
%S A132462 1,0,1,1,0,2,1,1,3,2,2,5,2,4,7,4,7,10,6,11,14,9,17,19,14,25,26,21,36,
%T A132462 35,31,50,47,45,69,63,64,93,84,89,125,111,124,165,147,169,216,194,227,
%U A132462 281,254,303,363,332,400,466,432,523,595,559,680,756,721,876,956,926,1121
%N A132462 Number of partitions of n into distinct parts congruent to 0 or 2 modulo 3.
%H A132462 Reinhard Zumkeller, <a href="/A132462/b132462.txt">Table of n, a(n) for n = 0..200</a>
%F A132462 G.f.: Product_{k>=1} (1+x^(3*k))*(1+x^(3*k-1)). - _Emeric Deutsch_, Aug 30 2007
%F A132462 a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(23/12) * sqrt(3) * n^(3/4)). - _Vaclav Kotesovec_, Aug 24 2015
%e A132462 a(8)=3 because we have 8, 6+2 and 5+3.
%p A132462 g:=product((1+x^(3*k))*(1+x^(3*k-1)),k=1..30): gser:=series(g,x=0,100): seq(coeff(gser,x,n),n=0..70); # _Emeric Deutsch_, Aug 30 2007
%t A132462 nmax = 40; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 24 2015 *)
%Y A132462 Cf. A007494, A035361, A003105, A132463.
%K A132462 nonn
%O A132462 0,6
%A A132462 _Reinhard Zumkeller_, Aug 22 2007
%E A132462 a(0)=1 prepended by _Vaclav Kotesovec_, Aug 24 2015