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 A035651 #14 Aug 16 2020 20:23:35
%S A035651 0,0,0,0,0,0,0,1,1,1,1,1,1,1,4,4,4,4,4,4,4,10,11,11,11,11,11,11,22,25,
%T A035651 26,26,26,26,26,44,51,54,55,55,55,55,84,98,105,108,109,109,109,153,
%U A035651 178,193,200,203,204,204,270,313,341,356,363,366,367,463,532,582,611
%N A035651 Number of partitions of n into parts 7k and 7k+1 with at least one part of each type.
%H A035651 Robert Price, <a href="/A035651/b035651.txt">Table of n, a(n) for n = 1..1000</a>
%F A035651 G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 1)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - _Robert Price_, Aug 12 2020
%t A035651 nmax = 67; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 1;
%t A035651 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035651 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 12 2020 *)
%t A035651 nmax = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 12 2020 *)
%Y A035651 Cf. A035441-A035468, A035618-A035650, A035652-A035699.
%K A035651 nonn
%O A035651 1,15
%A A035651 _Olivier Gérard_