|
%I #15 Aug 16 2020 16:32:02
%S 0,0,1,1,2,4,5,7,11,14,19,26,33,43,55,70,88,111,137,170,208,256,311,
%T 378,456,551,658,790,940,1119,1325,1570,1847,2179,2554,2996,3499,4088,
%U 4753,5533,6414,7436,8593,9931,11439,13180,15140,17391,19926,22827
%N Number of partitions of n into parts 3k+1 and 3k+2 with at least one part of each type.
%H Alois P. Heinz, <a href="/A035620/b035620.txt">Table of n, a(n) for n = 1..1000</a> (first 80 terms from Robert Price)
%F G.f.: (-1 + 1/Product_{k>=0} (1 - x^(3 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(3 k + 2))). - _Robert Price_, Aug 16 2020
%t nmax = 50; s1 = Range[0, nmax/3]*3 + 1; s2 = Range[0, nmax/3]*3 + 2;
%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],
%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)
%t nmax = 50; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(3 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* _Robert Price_, Aug 16 2020*)
%Y Cf. A035441-A035468, A035618-A035619, A035621-A035699.
%K nonn
%O 1,5
%A _Olivier Gérard_
|
