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 A035669 #19 Jan 03 2025 09:27:54
%S A035669 0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,2,1,1,1,2,3,1,4,3,3,3,5,7,4,7,7,8,8,10,
%T A035669 13,10,14,15,16,17,20,25,21,26,29,32,33,37,45,41,47,54,58,61,65,79,76,
%U A035669 83,94,103,108,113,132,135,143,160,172,185,192,219,227,240,265,286
%N A035669 Number of partitions of n into parts 7k+4 and 7k+5 with at least one part of each type.
%H A035669 Robert Price, <a href="/A035669/b035669.txt">Table of n, a(n) for n = 1..1000</a>
%F A035669 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7*k + 4)))*(-1 + 1/Product_{k>=0} (1 - x^(7*k + 5))). - _Robert Price_, Aug 15 2020
%t A035669 nmax = 74; s1 = Range[0, nmax/7]*7 + 4; s2 = Range[0, nmax/7]*7 + 5;
%t A035669 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035669 nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020 *)
%Y A035669 Cf. A035441-A035468, A035618-A035668, A035670-A035699.
%K A035669 nonn
%O A035669 1,16
%A A035669 _Olivier Gérard_