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 A035671 #17 Jan 03 2025 09:28:06
%S A035671 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,2,0,0,1,1,3,2,3,1,1,3,3,6,5,5,3,3,
%T A035671 7,8,11,9,8,7,9,15,15,19,16,15,16,19,27,28,32,28,27,32,36,48,48,52,49,
%U A035671 49,58,65,80,81,85,84,84,101,111,131,132,137,138,143,169,184,208,213
%N A035671 Number of partitions of n into parts 7k+5 and 7k+6 with at least one part of each type.
%H A035671 Robert Price, <a href="/A035671/b035671.txt">Table of n, a(n) for n = 1..1000</a>
%F A035671 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7*k + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(7*k + 6))). - _Robert Price_, Aug 15 2020
%t A035671 nmax = 78; s1 = Range[0, nmax/7]*7 + 5; s2 = Range[0, nmax/7]*7 + 6;
%t A035671 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035671 nmax = 78; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020 *)
%Y A035671 Cf. A035441-A035468, A035618-A035670, A035672-A035699.
%K A035671 nonn
%O A035671 1,18
%A A035671 _Olivier Gérard_