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%I #10 Nov 23 2020 08:25:45
%S 1,0,1,0,0,1,0,2,1,0,2,1,0,4,1,6,4,1,6,6,1,12,6,1,18,8,25,24,8,25,30,
%T 10,49,42,10,73,48,12,121,60,132,145,72,134,217,84,254,265,96,376,361,
%U 114,616,433,126,858,553,864,1218,649,882,1580,817,1620,2180,937
%N Number of compositions (ordered partitions) of n into distinct parts congruent to 2 mod 3.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{k>=0} k! * x^(k*(3*k + 1)/2) / Product_{j=1..k} (1 - x^(3*j)).
%e a(15) = 6 because we have [8, 5, 2], [8, 2, 5], [5, 8, 2], [5, 2, 8], [2, 8, 5] and [2, 5, 8].
%t nmax = 65; CoefficientList[Series[Sum[k! x^(k (3 k + 1)/2)/Product[1 - x^(3 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000931, A016789, A032020, A032021, A035386, A262928, A337547, A339059, A339060.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Nov 22 2020
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