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%I #12 May 20 2024 08:57:11
%S 0,0,1,1,0,1,1,1,3,3,3,5,5,5,8,9,9,13,15,17,23,26,29,36,41,46,57,64,
%T 72,87,98,111,131,149,168,197,223,251,291,328,369,423,476,534,609,683,
%U 765,867,970,1084,1222,1365,1522,1710,1905,2121,2374,2639,2931,3269,3627,4020,4471,4950
%N Number of distinct partitions p of n such that max(p) == 2 mod 3.
%F G.f.: Sum_{k>=0} x^(3*k+2) * Product_{j=1..3*k+1} (1+x^j).
%F A000009(n) = A372893(n) + A373012(n) + a(n).
%e a(8) = 3 counts these partitions: 8, 53, 521.
%o (PARI) my(N=70, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)*prod(j=1, 3*k+1, 1+x^j))))
%Y Cf. A000009, A372893, A373012.
%K nonn
%O 0,9
%A _Seiichi Manyama_, May 20 2024
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