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A295218
Number of partitions of 2*n-1 into four squares.
1
1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3, 4, 2, 4, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 2, 5, 5, 4, 3, 6, 4, 5, 4, 5, 5, 5, 3, 6, 6, 5, 5, 6, 4, 5, 5, 5, 6, 8, 4, 6, 6, 7, 5, 7, 5, 7, 7, 6, 6, 6, 5, 8, 8, 6, 5, 10, 6, 8, 6, 7, 7, 8, 5, 8, 10, 7, 8, 8, 6, 8, 7, 9, 9, 11, 5, 8, 10, 7, 7
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
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
Sequence in context: A291150 A292375 A361702 * A338430 A223135 A084113
KEYWORD
nonn
AUTHOR
STATUS
approved