Representation of integer as sum of squares

kpatsak · 2007-10-26, 18:38

Is there a formula that gives the number of representations of n as a sum four squares? Any help would be more than appreciated.

cheesehead · 2007-10-27, 09:22

If you haven't already seen it, let me introduce you to The On-Line Encyclopedia of Integer Sequences (OEIS) at http://www.research.att.com/~njas/sequences/. (If you have seen it, did you know you could use its search function on words, not just numbers?) Try OEIS search on "sum four squares".

kpatsak · 2007-10-27, 10:26

I have seen this encyclopedia, moreover I have searched it.
It doesn't contain the sequence that I want and for many of the sequences it does not contain it's formula

R. Gerbicz · 2007-10-27, 22:10

Quote:

Originally Posted by kpatsak

Is there a formula that gives the number of representations of n as a sum four squares? Any help would be more than appreciated.

It's well known: f[n]=8*sum((d|n)&&(d%4>0),d)
See:
http://mathworld.wolfram.com/SumofSquaresFunction.html

cheesehead · 2007-10-29, 17:53

Quote:

Originally Posted by kpatsak

I have seen this encyclopedia, moreover I have searched it.
It doesn't contain the sequence that I want and for many of the sequences it does not contain it's formula

When I searched OEIS on "sum four squares" the second page of returned results included

http://www.research.att.com/~njas/sequences/A000118 "Number of ways of writing n as a sum of 4 squares"

which looks like "number of representations of n as a sum four squares". Among the several given formulas seems (to me) to be one equivalent to what R. Gerbicz quoted above.

If A000118 (1,8,24,32,24,48,96,64,24,104,144,96,96,112,...) isn't what you want, can you list a few specific values of what you seek?

2007-10-26, 18:38	#1
kpatsak Oct 2007 3 Posts	Representation of integer as sum of squares Is there a formula that gives the number of representations of n as a sum four squares? Any help would be more than appreciated.

2007-10-27, 09:22	#2
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 7692₁₀ Posts	If you haven't already seen it, let me introduce you to The On-Line Encyclopedia of Integer Sequences (OEIS) at http://www.research.att.com/~njas/sequences/. (If you have seen it, did you know you could use its search function on words, not just numbers?) Try OEIS search on "sum four squares". Last fiddled with by cheesehead on 2007-10-27 at 09:25

2007-10-27, 10:26	#3
kpatsak Oct 2007 3₁₀ Posts	The encyclopedia I have seen this encyclopedia, moreover I have searched it. It doesn't contain the sequence that I want and for many of the sequences it does not contain it's formula

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