A339376 Number of partitions of n into an odd number of distinct triangular numbers.

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, 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, 4, 1, 5, 4, 2, 3, 5, 3, 6, 4, 2, 6, 4, 3, 5, 6, 5, 5, 5, 5, 5, 4, 5

Offset

0,11

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(28) = 3 because we have [28], [21, 6, 1] and [15, 10, 3].

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

Sequence in context: A285108 A030216 A357352 * A362425 A159459 A304095

Adjacent sequences: A339373 A339374 A339375 * A339377 A339378 A339379

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved