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 A035386 #38 Jun 17 2023 22:55:20
%S A035386 1,0,1,0,1,1,1,1,2,1,3,2,3,3,4,4,6,5,7,7,9,9,12,11,15,15,18,19,23,23,
%T A035386 29,29,35,37,43,45,53,55,64,68,78,82,95,99,114,121,136,145,164,173,
%U A035386 196,208,232,248,276,294,328,349,386,413,456,486,537,572,629,673,737,787
%N A035386 Number of partitions of n into parts congruent to 2 mod 3.
%C A035386 a(n) = A116376(3*n). - _Reinhard Zumkeller_, Feb 15 2006
%H A035386 Vaclav Kotesovec, <a href="/A035386/b035386.txt">Table of n, a(n) for n = 0..10000</a>
%H A035386 James Mc Laughlin, Andrew V. Sills, Peter Zimmer, <a href="https://doi.org/10.37236/36">Rogers-Ramanujan-Slater Type Identities </a>, arXiv:1901.00946 [math.NT]
%F A035386 a(n) = 1/n*Sum_{k=1..n} A078182(k)*a(n-k), a(0) = 1. - _Vladeta Jovovic_, Nov 21 2002
%F A035386 Euler transform of period 3 sequence [ 0, 1, 0, ...]. - _Michael Somos_, Jul 24 2007
%F A035386 a(n) ~ Gamma(2/3) * exp(sqrt(2*n)*Pi/3) / (2^(11/6) * sqrt(3) * Pi^(1/3) * n^(5/6)) * (1 + (Pi/72 - 5/(3*Pi)) / sqrt(2*n)). - _Vaclav Kotesovec_, Feb 26 2015, extended Jan 24 2017
%F A035386 G.f.: A(x) = Sum_{n >= 0} x^(n*(3*n-1))/Product_{k = 1..n} ((1 - x^(3*k)) *(1 - x^(3*k-1))). (Set z = x^2 and q = x^3 in Mc Laughlin et al., Section 1.3, Entry 7.) - _Peter Bala_, Feb 02 2021
%p A035386 g:=add(x^(n*(3*n-1))/mul((1-x^(3*k))*(1-x^(3*k-1)), k = 1..n), n = 0..6): gser:=series(g,x,101): seq(coeff(gser,x,n), n = 0..100); # _Peter Bala_, Feb 02 2021
%t A035386 nmax=100; CoefficientList[Series[Product[1/(1-x^(3*k+2)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 26 2015 *)
%t A035386 nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 3] == 2, Do[poly[[j + 1]] -= poly[[j - k + 1]], {j, nmax, k, -1}];], {k, 2, nmax}]; poly2 = Take[poly, {2, nmax + 1}]; poly3 = 1 + Sum[poly2[[n]]*x^n, {n, 1, Length[poly2]}]; CoefficientList[Series[1/poly3, {x, 0, Length[poly2]}], x] (* _Vaclav Kotesovec_, Jan 13 2017 *)
%t A035386 nmax = 50; s = Range[0, nmax/3]*3 + 2;
%t A035386 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* _Robert Price_, Aug 05 2020 *)
%o A035386 (PARI) {a(n)= if( n<0, 0, polcoeff( 1 / prod( k=1, n, 1 - (k%3==2) * x^k, 1 + x * O(x^n)), n))} /* _Michael Somos_, Jul 24 2007 */
%Y A035386 Cf. A035382, A035451, A262928.
%K A035386 nonn,easy
%O A035386 0,9
%A A035386 _Olivier Gérard_