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 A035647 #16 Aug 16 2020 20:12:48
%S A035647 0,0,0,0,0,1,0,1,0,2,0,4,0,5,0,7,0,11,0,14,0,19,0,26,0,33,0,43,0,55,0,
%T A035647 70,0,88,0,111,0,137,0,170,0,208,0,256,0,311,0,378,0,456,0,551,0,658,
%U A035647 0,790,0,940,0,1119,0,1325,0,1570,0,1847,0,2179,0,2554,0,2996,0,3499
%N A035647 Number of partitions of n into parts 6k+2 and 6k+4 with at least one part of each type.
%H A035647 Robert Price, <a href="/A035647/b035647.txt">Table of n, a(n) for n = 1..1000</a>
%F A035647 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 4))). - _Robert Price_, Aug 16 2020
%t A035647 nmax = 74; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 4;
%t A035647 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035647 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 13 2020 *)
%t A035647 nmax = 74; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020 *)
%Y A035647 Cf. A035441-A035468, A035618-A035646, A035648-A035699.
%Y A035647 Bisections give A035620 (even part), A000004 (odd part).
%K A035647 nonn
%O A035647 1,10
%A A035647 _Olivier Gérard_