This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373015 #11 May 20 2024 08:57:21
%S A373015 0,0,1,1,2,3,4,5,8,10,14,19,25,33,45,58,76,99,127,162,209,263,333,419,
%T A373015 524,652,813,1003,1239,1524,1868,2281,2786,3382,4104,4965,5993,7213,
%U A373015 8676,10396,12447,14866,17725,21087,25063,29711,35185,41589,49089,57839,68079
%N A373015 Number of partitions p of n such that max(p) == 2 mod 3.
%F A373015 G.f.: Sum_{k>=0} x^(3*k+2) / Product_{j=1..3*k+2} (1-x^j).
%F A373015 A000041(n) = A363045(n) + A373014(n) + a(n).
%e A373015 a(8) = 8 counts these partitions: 8, 53, 521, 5111, 2222, 22211, 221111, 2111111.
%o A373015 (PARI) my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)/prod(j=1, 3*k+2, 1-x^j))))
%Y A373015 Cf. A000041, A363045, A373014.
%K A373015 nonn
%O A373015 0,5
%A A373015 _Seiichi Manyama_, May 20 2024