A339376 - OEIS

%I #4 Dec 02 2020 09:01:29

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

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

%U 4,1,5,4,2,3,5,3,6,4,2,6,4,3,5,6,5,5,5,5,5,4,5

%N Number of partitions of n into an odd 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(28) = 3 because we have [28], [21, 6, 1] and [15, 10, 3].

%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, A067659, A292518, A339367, A339373, A339374, A339375.

%K nonn

%O 0,11

%A _Ilya Gutkovskiy_, Dec 02 2020