A339375 - OEIS

%I #6 Dec 02 2020 09:01:23

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

%T 2,1,1,1,3,1,2,0,2,2,0,2,3,3,1,2,2,2,2,2,1,4,4,1,3,2,3,2,3,1,5,4,2,4,

%U 2,4,4,3,2,6,4,3,4,5,2,3,6,5,6,5,4,5,5,4,5,6,4

%N Number of partitions of n into an even number of distinct triangular numbers.

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

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

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

%F a(n) = (A024940(n) + A292518(n)) / 2.

%e a(31) = 3 because we have [28, 3], [21, 10] and [21, 6, 3, 1].

%t nmax = 90; CoefficientList[Series[(1/2) (Product[(1 + x^(k (k + 1)/2)), {k, 1, nmax}] + Product[(1 - x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A000217, A024940, A067661, A292518, A339366, A339373, A339374, A339376.

%K nonn

%O 0,17

%A _Ilya Gutkovskiy_, Dec 02 2020