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A030272 Number of partitions of n^3 into distinct cubes. 18
1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 4, 6, 6, 7, 6, 20, 18, 21, 42, 55, 52, 80, 126, 140, 201, 323, 361, 600, 626, 938, 1387, 1648, 2310, 3620, 4575, 5495, 9278, 11239, 14229, 23406, 28780, 38218, 53987, 73114, 87568, 134007, 181986, 233004, 348230, 432184 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..180

FORMULA

a(n) = [x^(n^3)] Product_{k>=1} (1 + x^(k^3)). - Ilya Gutkovskiy, Apr 13 2017

a(n) = A279329(n^3). - Vaclav Kotesovec, May 06 2019

a(n) ~ exp(2^(7/4) * 3^(-3/2) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(3/4)) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/8) / (2^(17/8) * 3^(1/4) * sqrt(Pi) * n^(21/8)). - Vaclav Kotesovec, May 06 2019

EXAMPLE

a(6) = 2: [27,64,125], [216].

a(9) = 3: [1,27,64,125,512], [1,216,512], [729].

PROG

(PARI) apply( A030272(n)=A279329(n^3), [0..30]) \\ M. F. Hasler, Jan 05 2020

CROSSREFS

Cf. A000009, A003108, A033461, A259792, A279329.

Sequence in context: A305499 A210873 A224838 * A157128 A301376 A307828

Adjacent sequences:  A030269 A030270 A030271 * A030273 A030274 A030275

KEYWORD

nonn

AUTHOR

Warren D. Smith

EXTENSIONS

a(0)=1 prepended by Ilya Gutkovskiy, Apr 13 2017

STATUS

approved

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Last modified February 27 09:24 EST 2020. Contains 332301 sequences. (Running on oeis4.)