|
| |
|
|
A119395
|
|
Number of nonnegative integer solutions to the equation x^2+3y^2=n.
|
|
1
| |
|
|
1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 3, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 1, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| The number of integer solutions is given by A033716.
|
|
|
FORMULA
| For n>0, a(n)=(A033716(n)+2)/4 if n is a square or a triple of a square; otherwise a(n)=A033716(n)/4. Alternatively, a(n)=ceil(A033716(n)/4).
|
|
|
PROG
| (PARI) { A033716(n) = local(f, B); f=factorint(n); B=1; for(i=1, matsize(f)[1], if(f[i, 1]%3==1, B*=f[i, 2]+1); if(f[i, 1]%3==2, if(f[i, 2]%2, return(0)))); if(n%4, 2*B, 6*B) } { a(n) = ceil(A033716(n)/4) }
|
|
|
CROSSREFS
| Cf. A033716, A096936.
Sequence in context: A102082 A030199 A005089 * A087476 A035162 A121454
Adjacent sequences: A119392 A119393 A119394 * A119396 A119397 A119398
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), May 16 2006
|
| |
|
|
