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 A035628 #18 Aug 16 2020 17:07:25
%S A035628 0,0,0,0,0,0,1,0,1,0,1,3,1,3,1,3,7,3,8,3,8,14,8,17,8,18,26,18,33,18,
%T A035628 36,47,37,61,37,68,81,71,106,72,121,138,128,181,131,209,228,224,297,
%U A035628 231,347,372,376,482,391,566,592,619,760,648,898,934,989,1188,1043
%N A035628 Number of partitions of n into parts 5k and 5k+2 with at least one part of each type.
%H A035628 Robert Price, <a href="/A035628/b035628.txt">Table of n, a(n) for n = 1..1000</a>
%F A035628 G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+2)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - _Robert Price_, Aug 07 2020
%t A035628 nmax = 65; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 2;
%t A035628 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035628 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035628 nmax = 65; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 06 2020 *)
%Y A035628 Cf. A035441-A035468, A035618-A035627, A035629-A035699.
%K A035628 nonn
%O A035628 1,12
%A A035628 _Olivier Gérard_