A173682 -id:A173682 - cp's OEIS frontend

A282288 Expansion of (Sum_{k>=0} x^(k^4))^19.

1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 988, 513, 2926, 15505, 58140, 162792, 352716, 604656, 831402, 923780, 831402, 604656, 352716, 162792, 58140, 15504, 3078, 3249, 23275, 116280, 406980, 1058148, 2116296, 3325608, 4157010, 4157010, 3325608

Offset: 0

Ilya Gutkovskiy, Feb 12 2017

Number of ways to write n as an ordered sum of 19 fourth powers (A000583).
a(n) > 0 for all n >= 0.
Every natural number is the sum of at most 19 fourth powers (Balasubramanian, 1986).

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Biquadratic Number
Eric Weisstein's World of Mathematics, Waring's Problem

Cf. A000583, A002377, A002804, A014110, A173682.

nmax = 42; CoefficientList[Series[Sum[x^k^4, {k, 0, nmax}]^19, {x, 0, nmax}], x]

G.f.: (Sum_{k>=0} x^(k^4))^19.

A069136 Numbers that are not the sum of 5 nonnegative cubes.

Original entry on oeis.org

6, 7, 13, 14, 15, 20, 21, 22, 23, 34, 39, 41, 42, 46, 47, 48, 49, 50, 53, 58, 60, 61, 69, 76, 77, 79, 84, 85, 86, 87, 95, 98, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 117, 121, 122, 123, 124, 132, 139, 140, 147, 148, 151, 158, 159, 165

Offset: 1

N. J. A. Sloane, Apr 08 2002

nonn

Sequence is conjectured to be finite.

Comment from Richard C. Schroeppel, Sep 22 2010: It is conjectured that 7373170279850 is the largest number requiring more than four cubes (see Deshouillers et al.).

Bohman, Jan and Froberg, Carl-Erik; Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
F. Romani, Computations concerning Waring's problem, Calcolo, 19 (1982), 415-431.

T. D. Noe, Table of n, a(n) for n=1..4060
Jean-Marc Deshouillers, Francois Hennecart and Bernard Landreau; appendix by I. Gusti Putu Purnaba, 7373170279850, Math. Comp. 69 (2000), 421-439.
Index entries for sequences related to sums of cubes

Sums of k cubes, number of ways of writing n as, for k=1..9: A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

cp's OEIS Frontend

A282288 Expansion of (Sum_{k>=0} x^(k^4))^19.

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