A264393 Number of partitions of n having no perfect cube parts (n>=0).

1, 0, 1, 1, 2, 2, 4, 4, 6, 8, 11, 13, 19, 22, 30, 37, 48, 58, 76, 91, 116, 141, 176, 212, 265, 317, 390, 468, 571, 681, 828, 983, 1185, 1407, 1685, 1993, 2378, 2802, 3326, 3913, 4624, 5421, 6387, 7466, 8762, 10223, 11955, 13910, 16225, 18831, 21898, 25365

Offset

0,5

Comments

a(n) = A264391(n,0).

Convolution of A279484 and A000041. - Vaclav Kotesovec, Dec 30 2016

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{i>=1}(1-x^(h(i)))/(1-x^i), where h(i) = i^3.

a(n) ~ exp(Pi*sqrt(2*n/3) - 2^(1/6) * Gamma(1/3) * Zeta(4/3) * n^(1/6) / (3^(5/6) * Pi^(1/3))) * Pi / (6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Dec 30 2016

Example

a(7) = 4 because we have [7], [5,2], [4,3], and [3,2,2].

Maple

h := proc (i) options operator, arrow; i^3 end proc: g := product((1-x^h(i))/(1-x^i), i = 1 .. 150): gser := series(g, x = 0, 65): seq(coeff(gser, x, n), n = 0 .. 60);

Mathematica

nmax=100; CoefficientList[Series[Product[(1-x^(k^3))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 30 2016 *)

Crossrefs

Cf. A264391, A279484.

Sequence in context: A240012 A295261 A293627 * A362307 A094858 A327851

Adjacent sequences: A264390 A264391 A264392 * A264394 A264395 A264396

Keyword

nonn

Author

Emeric Deutsch, Nov 13 2015

Status

approved