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 A035653 #14 Aug 16 2020 20:26:52
%S A035653 0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,3,0,1,3,0,1,3,6,1,3,7,1,3,7,12,3,7,
%T A035653 15,3,7,16,21,7,16,28,7,16,31,36,16,32,50,16,32,57,60,32,60,85,32,61,
%U A035653 100,98,61,107,141,61,110,169,157,111,184,226,111,191,276,249,194,305
%N A035653 Number of partitions of n into parts 7k and 7k+3 with at least one part of each type.
%H A035653 Robert Price, <a href="/A035653/b035653.txt">Table of n, a(n) for n = 1..1000</a>
%F A035653 G.f. : (-1 + 1/Product_{k>=0} (1 - x^(7 k + 3)))*(-1 + 1/Product_{k>=1} (1 - x^(7 k))). - _Robert Price_, Aug 12 2020
%t A035653 nmax = 75; s1 = Range[1, nmax/7]*7; s2 = Range[0, nmax/7]*7 + 3;
%t A035653 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035653 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 12 2020 *)
%t A035653 nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 12 2020 *)
%Y A035653 Cf. A035441-A035468, A035618-A035652, A035654-A035699.
%K A035653 nonn
%O A035653 1,17
%A A035653 _Olivier Gérard_