A030272 Number of partitions of n^3 into distinct cubes.

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

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].

Mathematica

nmax = 50; poly = ConstantArray[0, nmax^3 + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[Do[poly[[j + 1]] += poly[[j - k^3 + 1]], {j, nmax^3, k^3, -1}]; , {k, 2, nmax}]; Table[poly[[1 + n^3]], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 19 2020 *)

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 A359899 A301376

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