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 A035629 #21 Aug 16 2020 17:05:59
%S A035629 0,0,0,0,0,0,0,1,0,0,1,0,3,1,0,3,1,6,3,1,7,3,12,7,3,15,7,21,16,7,28,
%T A035629 16,36,31,16,50,32,60,57,32,85,60,98,100,61,141,107,157,169,110,226,
%U A035629 184,249,276,191,358,305,388,442,320,554,495,598,691,524,848,782,911
%N A035629 Number of partitions of n into parts 5k and 5k+3 with at least one part of each type.
%H A035629 Robert Price, <a href="/A035629/b035629.txt">Table of n, a(n) for n = 1..1000</a>
%F A035629 G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+3)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - _Robert Price_, Aug 06 2020
%t A035629 nmax = 68; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 3;
%t A035629 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035629 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035629 nmax = 68; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 3)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 06 2020 *)
%Y A035629 Cf. A035441-A035468, A035618-A035628, A035630-A035699.
%K A035629 nonn
%O A035629 1,13
%A A035629 _Olivier Gérard_