A285445 Expansion of Product_{k>=1} (1 + x^k) / (1 - x^(3*k)).

1, 1, 1, 3, 3, 4, 8, 9, 11, 19, 22, 27, 42, 49, 60, 87, 102, 124, 172, 202, 244, 326, 383, 460, 598, 702, 838, 1066, 1249, 1483, 1854, 2167, 2560, 3154, 3677, 4324, 5264, 6120, 7165, 8633, 10009, 11671, 13939, 16116, 18720, 22188, 25583, 29611, 34862, 40089

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Mircea Merca, Partitions with modular multiplicities, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 120, 80 (2026). See p. 3.

Formula

a(n) ~ exp(sqrt(5*n)*Pi/3) * sqrt(5) / (8*sqrt(3)*n).

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1-x^(3*k))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A266648, A285446.

Sequence in context: A137417 A137418 A357306 * A327745 A155822 A160646

Adjacent sequences: A285442 A285443 A285444 * A285446 A285447 A285448

Keyword

nonn

Author

Vaclav Kotesovec, Apr 19 2017

Status

approved