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%I #24 Aug 03 2020 01:34:00
%S 1,1,1,2,3,3,5,7,8,11,15,17,23,30,35,44,57,66,82,103,121,146,181,211,
%T 253,308,360,425,513,596,700,834,969,1127,1333,1541,1786,2093,2415,
%U 2781,3241,3723,4273,4946,5669,6476,7461,8519,9705,11123,12669,14379,16418
%N Number of partitions of n into parts 3k or 3k+1.
%C Euler transform of period 3 sequence [ 1, 0, 1, ...]. - _Kevin T. Acres_, Apr 28 2018
%H Robert Price, <a href="/A035360/b035360.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ Gamma(1/3) * exp(2*Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(2/3) * n^(11/12)). - _Vaclav Kotesovec_, Aug 23 2015
%e 1 + x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 7*x^7 + 8*x^8 + 11*x^9 + ...
%t nmax = 50; CoefficientList[Series[Product[1/((1 - x^(3*k))*(1 - x^(3*k-2))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 23 2015 *)
%t nmax = 52; kmax = nmax/3;
%t s = Flatten[{Range[0, kmax]*3}~Join~{Range[0, kmax]*3 + 1}];
%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* _Robert Price_, Aug 02 2020 *)
%Y Cf. A032766, A132463, A000726, A035361.
%K nonn
%O 0,4
%A _Olivier Gérard_
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