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 A035666 #17 Jan 03 2025 10:57:23
%S A035666 0,0,0,0,0,0,1,0,0,1,1,0,1,3,1,1,3,3,2,3,6,4,4,7,8,6,8,13,10,10,16,17,
%T A035666 14,19,25,22,23,32,34,31,38,48,45,47,60,65,62,73,86,86,90,109,117,117,
%U A035666 133,153,155,165,191,205,209,235,261,272,288,326,349,362,398,440,459
%N A035666 Number of partitions of n into parts 7k+3 and 7k+4 with at least one part of each type.
%H A035666 Alois P. Heinz, <a href="/A035666/b035666.txt">Table of n, a(n) for n = 1..1000</a>
%F A035666 G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7*k + 3)))*(-1 + 1/Product_{k>=0} (1 - x^(7*k + 4))). - _Robert Price_, Aug 15 2020
%t A035666 nmax = 71; s1 = Range[0, nmax/7]*7 + 3; s2 = Range[0, nmax/7]*7 + 4;
%t A035666 Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t A035666 x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 15 2020 *)
%t A035666 nmax = 71; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 3)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 4)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 15 2020*)
%Y A035666 Cf. A035441-A035468, A035618-A035665, A035667-A035699.
%K A035666 nonn
%O A035666 1,14
%A A035666 _Olivier Gérard_