login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264393 Number of partitions of n having no perfect cube parts (n>=0). 5
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 (list; graph; refs; listen; history; text; internal format)
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 * A094858 A029940 A045674

Adjacent sequences:  A264390 A264391 A264392 * A264394 A264395 A264396

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 13 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 11:04 EST 2018. Contains 299536 sequences. (Running on oeis4.)