A339373 Number of partitions of n into an even number of triangular numbers.

1, 0, 1, 0, 2, 0, 3, 1, 3, 2, 4, 3, 6, 5, 6, 6, 10, 7, 13, 10, 15, 13, 20, 15, 26, 21, 28, 26, 36, 31, 44, 42, 49, 50, 61, 57, 75, 73, 84, 85, 103, 97, 123, 121, 137, 140, 166, 159, 194, 194, 216, 225, 256, 253, 295, 304, 330, 346, 389, 387, 446, 456, 498, 516, 579, 576

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

Formula

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

a(n) = (A007294(n) + A292519(n)) / 2.

Example

a(6) = 3 because we have [3, 3], [3, 1, 1, 1] and [1, 1, 1, 1, 1, 1].

Mathematica

nmax = 65; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k (k + 1)/2)), {k, 1, nmax}] + Product[1/(1 + x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000217, A007294, A027187, A292519, A339364, A339374, A339375, A339376.

Sequence in context: A162201 A271722 A029219 * A212217 A211857 A292803

Adjacent sequences: A339370 A339371 A339372 * A339374 A339375 A339376

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved