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 A035693 #12 Aug 16 2020 14:10:07
%S A035693 0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,1,2,1,1,2,1,1,3,3,4,3,3,5,3,4,7,7,8,
%T A035693 7,8,10,8,10,15,14,15,16,16,20,18,21,29,27,28,32,33,36,37,42,51,50,52,
%U A035693 59,60,66,69,77,90,88,93,105,107,115,124,135,152,153,160,180,183,195
%N A035693 Number of partitions of n into parts 8k+3 and 8k+7 with at least one part of each type.
%H A035693 Robert Price, <a href="/A035693/b035693.txt">Table of n, a(n) for n = 1..1000</a>
%F A035693 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - _Robert Price_, Aug 15 2020
%t A035693 nmax = 77; s1 = Range[0, nmax/8]*8 + 3; s2 = Range[0, nmax/8]*8 + 7;
%t A035693 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035693 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035693 nmax = 77; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035693 Cf. A035441-A035468, A035618-A035693, A035694-A035699.
%K A035693 nonn
%O A035693 1,18
%A A035693 _Olivier Gérard_