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 A035619 #15 Aug 16 2020 16:31:45
%S A035619 0,0,0,0,1,0,1,3,1,3,7,3,8,14,8,17,26,18,33,47,36,61,81,68,106,137,
%T A035619 121,181,224,209,296,362,347,478,570,565,750,890,894,1166,1360,1396,
%U A035619 1774,2062,2134,2677,3076,3228,3973,4555,4804,5854,6657,7085,8513
%N A035619 Number of partitions of n into parts 3k and 3k+2 with at least one part of each type.
%H A035619 Alois P. Heinz, <a href="/A035619/b035619.txt">Table of n, a(n) for n = 1..1000</a> (first 80 terms from Robert Price)
%F A035619 G.f.: (-1 + 1/Product_{k>=1} (1 - x^(3 k)))*(-1 + 1/Product_{k>=0} (1 - x^(3 k + 2))). - _Robert Price_, Aug 16 2020
%t A035619 nmax = 55; s1 = Range[1, nmax/3]*3; s2 = Range[0, nmax/3]*3 + 2;
%t A035619 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035619 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t A035619 nmax = 55; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(3 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y A035619 Cf. A035441-A035468, A035618, A035620-A035699.
%K A035619 nonn
%O A035619 1,8
%A A035619 _Olivier Gérard_