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A132463 Number of partitions of n into distinct parts congruent to 0 or 1 modulo 3.

%I A132463 #20 Oct 27 2023 20:06:53
%S A132463 1,1,0,1,2,1,1,3,2,2,5,4,3,7,7,5,10,11,8,14,17,13,20,25,19,27,36,29,
%T A132463 37,50,43,51,69,61,69,94,86,93,126,120,125,167,164,167,220,222,222,
%U A132463 287,297,294,373,393,386,481,516,505,617,672,657,788,868,850,1002,1114,1094
%N A132463 Number of partitions of n into distinct parts congruent to 0 or 1 modulo 3.
%H A132463 Alois P. Heinz, <a href="/A132463/b132463.txt">Table of n, a(n) for n = 0..1000</a> (first 201 terms from Reinhard Zumkeller)
%F A132463 G.f.: Product(k>=1, (1+x^(3*k))*(1+x^(3*k-2)) ). - _Emeric Deutsch_, Aug 26 2007
%F A132463 a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(19/12) * sqrt(3) * n^(3/4)). - _Vaclav Kotesovec_, Aug 24 2015
%e A132463 a(7)=3 because we have 7, 61 and 43.
%p A132463 g:=product((1+x^(3*k))*(1+x^(3*k-2)),k=1..30): gser:=series(g,x=0,100): seq(coeff(gser,x,n),n=0..65); # _Emeric Deutsch_, Aug 26 2007
%t A132463 nmax = 100; CoefficientList[Series[Product[((1+x^(3*k))*(1+x^(3*k-2))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 24 2015 *)
%Y A132463 Cf. A032766, A035360, A003105, A132462.
%K A132463 nonn
%O A132463 0,5
%A A132463 _Reinhard Zumkeller_, Aug 22 2007
%E A132463 Prepended a(0) = 1, _Joerg Arndt_, Feb 22 2015