OFFSET
0,2
COMMENTS
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).
LINKS
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
FORMULA
G.f.: (Sum_{k>=0} x^(k^4))^19.
MATHEMATICA
nmax = 42; CoefficientList[Series[Sum[x^k^4, {k, 0, nmax}]^19, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Feb 12 2017
STATUS
approved