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%I #20 Oct 27 2023 20:06:53
%S 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 37,50,43,51,69,61,69,94,86,93,126,120,125,167,164,167,220,222,222,
%U 287,297,294,373,393,386,481,516,505,617,672,657,788,868,850,1002,1114,1094
%N Number of partitions of n into distinct parts congruent to 0 or 1 modulo 3.
%H 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 G.f.: Product(k>=1, (1+x^(3*k))*(1+x^(3*k-2)) ). - _Emeric Deutsch_, Aug 26 2007
%F a(n) ~ exp(Pi*sqrt(2*n)/3) / (2^(19/12) * sqrt(3) * n^(3/4)). - _Vaclav Kotesovec_, Aug 24 2015
%e a(7)=3 because we have 7, 61 and 43.
%p 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 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 Cf. A032766, A035360, A003105, A132462.
%K nonn
%O 0,5
%A _Reinhard Zumkeller_, Aug 22 2007
%E Prepended a(0) = 1, _Joerg Arndt_, Feb 22 2015
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