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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]. 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

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