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 A373012 #12 May 20 2024 08:57:07
%S A373012 0,1,0,0,1,1,1,3,2,2,4,3,4,7,7,8,12,13,15,20,21,24,31,34,39,49,54,62,
%T A373012 76,84,97,116,130,148,174,195,221,257,287,325,374,419,472,540,604,679,
%U A373012 772,861,966,1092,1218,1362,1533,1706,1903,2133,2368,2635,2943,3263,3622,4033,4463
%N A373012 Number of distinct partitions p of n such that max(p) == 1 mod 3.
%F A373012 G.f.: Sum_{k>=0} x^(3*k+1) * Product_{j=1..3*k} (1+x^j).
%F A373012 A000009(n) = A372893(n) + a(n) + A373013(n).
%e A373012 a(7) = 3 counts these partitions: 7, 43, 421.
%o A373012 (PARI) my(N=70, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)*prod(j=1, 3*k, 1+x^j))))
%Y A373012 Cf. A000009, A372893, A373013.
%K A373012 nonn
%O A373012 0,8
%A A373012 _Seiichi Manyama_, May 20 2024