OFFSET
1,99
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(i) * c(k) * c(n-i-k), where c(n) is the characteristic function of squares (A010052).
MAPLE
N:= 100:
V:= Vector(N):
for a from 1 to floor(sqrt(N/3)) do
for b from a to floor(sqrt((N-a^2)/2)) do
R:= map(c -> a^2 + b^2 + c^2, [$b .. floor(sqrt(min(a^2+b^2-1, N-a^2-b^2)))]);
V[R]:= map(`+`, V[R], 1);
od od:
convert(V, list); # Robert Israel, Jan 01 2020
MATHEMATICA
Table[Sum[Sum[(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 10 2019
STATUS
approved