login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A305499 A210873 A224838 * A157128 A359899 A301376
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Ilya Gutkovskiy, Apr 13 2017
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 01:40 EST 2024. Contains 370522 sequences. (Running on oeis4.)