cp's OEIS Frontend

A035361 Number of partitions of n into parts 3k or 3k+2.

%I A035361 #22 Aug 03 2020 01:33:03
%S A035361 1,0,1,1,1,2,3,2,5,5,6,9,11,11,18,19,23,31,36,40,56,60,73,92,105,121,
%T A035361 155,170,204,247,280,325,397,440,521,615,695,805,954,1063,1244,1442,
%U A035361 1626,1873,2176,2431,2813,3221,3623,4146,4751,5309,6086,6905,7746,8807
%N A035361 Number of partitions of n into parts 3k or 3k+2.
%C A035361 Euler transform of period 3 sequence [ 0, 1, 1, ...]. - _Kevin T. Acres_, Apr 28 2018
%H A035361 Robert Price, <a href="/A035361/b035361.txt">Table of n, a(n) for n = 0..1000</a>
%F A035361 a(n) ~ Gamma(2/3) * exp(2*Pi*sqrt(n)/3) / (4 * sqrt(3) * n^(13/12) * Pi^(1/3)). - _Vaclav Kotesovec_, Aug 23 2015
%e A035361 1 + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 2*x^7 + 5*x^8 + 5*x^9 + 6*x^10 + ...
%t A035361 nmax = 50; CoefficientList[Series[Product[1/((1 - x^(3*k))*(1 - x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 23 2015 *)
%t A035361 nmax = 55; kmax = nmax/3;
%t A035361 s = Flatten[{Range[0, kmax]*3}~Join~{Range[0, kmax]*3 + 2}];
%t A035361 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* _Robert Price_, Aug 02 2020 *)
%Y A035361 Cf. A007494, A132462, A000726, A035360.
%K A035361 nonn
%O A035361 0,6
%A A035361 _Olivier Gérard_