|
|
A065458
|
|
Number of inequivalent (ordered) solutions to a^2 + b^2 + c^2 + d^2 = n^2.
|
|
4
|
|
|
1, 1, 2, 2, 2, 3, 4, 4, 2, 6, 7, 6, 4, 8, 10, 14, 2, 11, 14, 13, 7, 23, 15, 17, 4, 24, 21, 31, 10, 25, 37, 28, 2, 46, 29, 49, 14, 38, 35, 61, 7, 45, 62, 49, 15, 93, 47, 57, 4, 72, 67, 97, 21, 71, 84, 101, 10, 119, 70, 86, 37, 92, 79, 165, 2, 138, 127, 109, 29, 168, 140, 121, 14
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
a(5)=3 because 25 produces {0,0,0,5}, {0,0,3,4}, {1,2,2,4}.
|
|
MAPLE
|
N:= 100:
R:= Vector(N, 1):
for a from 0 to N do
for b from a to floor(sqrt(N^2-a^2)) do
for c from b to floor(sqrt(N^2-a^2-b^2)) do
q:= a^2 + b^2 + c^2;
for f in numtheory:-divisors(q) do
if f^2 + 2*f*c <= q and (f + q/f)::even then
r:= (f + q/f)/2;
if r <= N then R[r]:= R[r]+1 fi;
fi
od od od od:
|
|
MATHEMATICA
|
Length/@Table[SumOfSquaresRepresentations[4, (k)^2], {k, 72}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|