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 A035682 #16 Jan 03 2025 20:53:37
%S A035682 0,0,0,0,0,1,1,1,1,1,2,2,2,4,4,5,5,5,7,7,8,11,12,14,14,15,19,20,22,26,
%T A035682 29,34,35,37,43,46,51,57,63,72,76,81,91,98,107,117,128,144,153,163,
%U A035682 179,192,210,226,245,272,290,310,336,360,391,418,450,494,527,564,605
%N A035682 Number of partitions of n into parts 8k+1 and 8k+5 with at least one part of each type.
%H A035682 Alois P. Heinz, <a href="/A035682/b035682.txt">Table of n, a(n) for n = 1..1000</a>
%F A035682 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8*k + 5))). - _Robert Price_, Aug 15 2020
%t A035682 nmax = 67; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 5;
%t A035682 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035682 nmax = 67; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035682 Cf. A035441-A035468, A035618-A035681, A035683-A035699.
%K A035682 nonn
%O A035682 1,11
%A A035682 _Olivier Gérard_