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 A347867 #15 May 22 2024 15:12:47
%S A347867 1,2,3,4,6,10,14,20,27,38,51,70,92,123,162,212,274,355,453,579,733,
%T A347867 928,1165,1463,1822,2269,2808,3470,4266,5241,6407,7823,9514,11554,
%U A347867 13983,16900,20359,24494,29386,35205,42069,50206,59773,71069,84322,99913,118157,139556,164528,193734
%N A347867 Number of partitions of n such that 3*(greatest part) >= (number of parts).
%C A347867 Also, the number of partitions of n such that (greatest part) <= 3*(number of parts).
%F A347867 G.f.: Sum_{k>=1} x^k * Product_{j=1..k} (1-x^(3*k+j-1))/(1-x^j).
%o A347867 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(3*k+j-1))/(1-x^j))))
%Y A347867 Cf. A064174, A237755, A347868, A347869.
%Y A347867 Cf. A237756.
%K A347867 nonn
%O A347867 1,2
%A A347867 _Seiichi Manyama_, Jan 25 2022