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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A298434 Expansion of Product_{k>=1} 1/(1 - x^(k^3))^2. 4
 1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 17, 20, 23, 26, 29, 32, 38, 44, 50, 56, 62, 68, 74, 80, 90, 100, 110, 122, 134, 146, 158, 170, 187, 204, 221, 242, 263, 284, 305, 326, 353, 380, 407, 440, 473, 506, 539, 572, 612, 652, 692, 740, 788, 836, 887, 938, 997, 1056, 1115, 1184, 1253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of partitions of n into cubes of 2 kinds. Self-convolution of A003108. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{k>=1} 1/(1 - x^(k^3))^2. a(n) ~ exp(2^(11/4) * (Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(9/8) / (2^(27/8) * 3^(7/4) * Pi^(7/2) * n^(13/8)). - Vaclav Kotesovec, Apr 08 2018 EXAMPLE a(8) = 11 because we have [8a], [8b], [1a, 1a, 1a, 1a, 1a, 1a, 1a, 1a], [1a, 1a, 1a, 1a, 1a, 1a, 1a, 1b], [1a, 1a, 1a, 1a, 1a, 1a, 1b, 1b], [1a, 1a, 1a, 1a, 1a, 1b, 1b, 1b], [1a, 1a, 1a, 1a, 1b, 1b, 1b, 1b], [1a, 1a, 1a, 1b, 1b, 1b, 1b, 1b], [1a, 1a, 1b, 1b, 1b, 1b, 1b, 1b], [1a, 1b, 1b, 1b, 1b, 1b, 1b, 1b] and [1b, 1b, 1b, 1b, 1b, 1b, 1b, 1b]. MATHEMATICA nmax = 60; CoefficientList[Series[Product[1/(1 - x^(k^3))^2, {k, 1, Floor[nmax^(1/3) + 1]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 08 2018 *) CROSSREFS Cf. A000578, A000712, A003108, A279225. Sequence in context: A192588 A258946 A008815 * A200371 A246025 A211699 Adjacent sequences:  A298431 A298432 A298433 * A298435 A298436 A298437 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 19 2018 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 22:04 EST 2022. Contains 350466 sequences. (Running on oeis4.)