OFFSET
0,3
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..63 (terms 0..45 from Alois P. Heinz)
H. L. Fisher, Letter to N. J. A. Sloane, Mar 16 1989
G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proceedings of the London Mathematical Society, 2, XVI, 1917, p. 373.
FORMULA
a(n) = [x^(n^4)] Product_{j>=1} 1/(1-x^(j^4)). - Alois P. Heinz, Jul 10 2015
a(n) = A046042(n^4). - Vaclav Kotesovec, Aug 19 2015
a(n) ~ exp(5 * (Gamma(1/4)*Zeta(5/4))^(4/5) * n^(4/5) / 2^(16/5)) * (Gamma(1/4)*Zeta(5/4))^(4/5) / (2^(47/10) * sqrt(5) * Pi^(5/2) * n^(26/5)) [after Hardy & Ramanujan, 1917]. - Vaclav Kotesovec, Dec 29 2016
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
b(n, i-1) +`if`(i^4>n, 0, b(n-i^4, i)))
end:
a:= n-> b(n^4, n):
seq(a(n), n=0..23); # Alois P. Heinz, Jul 10 2015
MATHEMATICA
$RecursionLimit = 10^4; b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1] + If[i^4>n, 0, b[n-i^4, i]]]; a[n_] := b[n^4, n]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Dec 06 2016 after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 06 2015
EXTENSIONS
More terms from Alois P. Heinz, Jul 10 2015
STATUS
approved