A339375 Number of partitions of n into an even number of distinct triangular numbers.

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, 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, 2, 4, 4, 3, 2, 6, 4, 3, 4, 5, 2, 3, 6, 5, 6, 5, 4, 5, 5, 4, 5, 6, 4

Offset

0,17

Links

Table of n, a(n) for n=0..90.

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

Formula

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

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

Example

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

Mathematica

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]

Crossrefs

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

Sequence in context: A090465 A364357 A052344 * A147768 A167746 A360616

Adjacent sequences: A339372 A339373 A339374 * A339376 A339377 A339378

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved