A339369 - OEIS

%I #4 Dec 02 2020 01:01:24

%S 0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,2,2,2,3,2,3,2,3,2,4,

%T 2,4,3,4,3,4,4,4,4,5,4,5,4,5,4,6,4,6,5,6,5,7,6,7,6,8,6,8,7,8,8,9,8,9,

%U 9,9,9,10,10,11,10,12,10,12,11,12,12,14,12,14,13,14

%N Number of partitions of n into an odd number of cubes.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%F G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k^3)) - Product_{k>=1} 1 / (1 + x^(k^3))).

%F a(n) = (A003108(n) - A292560(n)) / 2.

%e a(17) = 2 because we have [8, 8, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

%t nmax = 85; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}] - Product[1/(1 + x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]

%Y Cf. A000578, A003108, A027193, A292560, A339365, A339368.

%K nonn

%O 0,18

%A _Ilya Gutkovskiy_, Dec 01 2020