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 A035683 #14 Jan 03 2025 20:53:30
%S A035683 0,0,0,0,0,0,1,1,1,1,1,1,2,2,4,4,4,4,5,5,7,7,10,11,12,12,14,14,18,19,
%T A035683 24,26,29,29,33,34,41,43,51,55,61,63,71,73,85,90,102,110,122,126,141,
%U A035683 146,164,174,194,207,230,239,263,275,304,322,355,377,414,433,473,495
%N A035683 Number of partitions of n into parts 8k+1 and 8k+6 with at least one part of each type.
%H A035683 Robert Price, <a href="/A035683/b035683.txt">Table of n, a(n) for n = 1..1000</a>
%F A035683 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8*k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(8*k + 6))). - _Robert Price_, Aug 15 2020
%t A035683 nmax = 68; s1 = Range[0, nmax/8]*8 + 1; s2 = Range[0, nmax/8]*8 + 6;
%t A035683 Table[Count[IntegerPartitions[n, All, s1~Join~s2], x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035683 nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035683 Cf. A035441-A035468, A035618-A035682, A035684-A035699.
%K A035683 nonn
%O A035683 1,13
%A A035683 _Olivier Gérard_