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 A373014 #13 May 20 2024 08:57:16
%S A373014 0,1,1,1,2,2,3,5,7,9,14,18,25,34,45,58,78,99,128,165,210,264,336,419,
%T A373014 525,655,813,1003,1242,1522,1867,2283,2783,3379,4105,4960,5989,7214,
%U A373014 8670,10391,12447,14858,17719,21088,25055,29705,35187,41581,49084,57844,68072,79974
%N A373014 Number of partitions p of n such that max(p) == 1 mod 3.
%F A373014 G.f.: Sum_{k>=0} x^(3*k+1) / Product_{j=1..3*k+1} (1-x^j).
%F A373014 A000041(n) = A363045(n) + a(n) + A373015(n).
%e A373014 a(7) = 5 counts these partitions: 7, 43, 421, 4111, 1111111.
%o A373014 (PARI) my(N=60, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)/prod(j=1, 3*k+1, 1-x^j))))
%Y A373014 Cf. A000041, A363045, A373015.
%Y A373014 Cf. A027193.
%K A373014 nonn
%O A373014 0,5
%A A373014 _Seiichi Manyama_, May 20 2024