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 A035680 #17 Jan 03 2025 09:27:50
%S A035680 0,0,0,1,1,1,2,2,2,3,3,5,6,6,8,9,9,11,12,15,18,19,23,26,27,31,34,39,
%T A035680 45,49,56,62,66,74,80,89,101,109,123,136,144,160,173,187,210,227,249,
%U A035680 275,293,319,346,371,408,442,480,525,562,608,655,701,763,822,887,963
%N A035680 Number of partitions of n into parts 8k+1 and 8k+3 with at least one part of each type.
%H A035680 Robert Price, <a href="/A035680/b035680.txt">Table of n, a(n) for n = 1..1000</a>
%F A035680 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8*k + 3))). - _Robert Price_, Aug 15 2020
%t A035680 nmax = 64; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 3;
%t A035680 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035680 nmax = 64; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020 *)
%Y A035680 Cf. A035441-A035468, A035618-A035679, A035681-A035699.
%K A035680 nonn
%O A035680 1,7
%A A035680 _Olivier Gérard_