OFFSET
1,5
COMMENTS
This is a bisection of A002635.
While A002635 contains each positive integer infinitely often, here a number can appear only finitely many times.
By the Jacobi theorem, a(n) >= A000203(n)/48 >= (1+n)/48, which implies the previous comment. - Robert Israel, Nov 21 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Jacobi four square theorem
MAPLE
N:= 100: # to get a(1)...a(N)
V:= Array(0..2*N-1):
for a from 0 while 4*a^2 <= 2*N-1 do
for b from a while a^2 + 3*b^2 <= 2*N-1 do
for c from b while a^2 + b^2 + 2*c^2 <= 2*N-1 do
for d from c while a^2 + b^2 + c^2 + d^2 <= 2*N-1 do
t:= a^2 + b^2 + c^2 + d^2;
V[t]:= V[t]+1
od od od od:
seq(V[2*i-1], i=1..N); # Robert Israel, Nov 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Nov 17 2017
STATUS
approved