OFFSET
0,2
COMMENTS
Number of integer triples (x,y,z) satisfying x^4+y^4+z^4 <= n, -n <= x,y,z <= n.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: (1 + 2*Sum_{j>0} x^(j^4))^3/(1-x). - Robert Israel, May 01 2019
MAPLE
N:= 100: # to get a(1)..a(N)
A:= Array(0..N):
for i from 0 while i^4 <= N do
if i=0 then ai:= 1 else ai:= 2 fi;
for j from 0 while i^4 + j^4 <= N do
if j=0 then aj:= 1 else aj:= 2 fi;
for k from 0 do
v:= i^4 + j^4 + k^4;
if v > N then break fi;
if k = 0 then ak:= 1 else ak:= 2 fi;
A[v]:= A[v] + ai*aj*ak;
od od od:
ListTools:-PartialSums(convert(A, list)); # Robert Israel, May 01 2019
PROG
(Python)
from math import isqrt
def A175376(n): return (f:=lambda m:1+(sum(isqrt(isqrt(m-t**4)) for t in range(isqrt(isqrt(m))+1))<<2))(n)+(sum(f(n-k**4) for k in range(1, isqrt(isqrt(n))+1))<<1) # Chai Wah Wu, Feb 23 2026
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 24 2010
STATUS
approved
