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Search: id:A096936
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| A096936 |
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Half of number of integer solutions to the equation x^2+3y^2=n. |
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+0
5
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| 1, 0, 1, 3, 0, 0, 2, 0, 1, 0, 0, 3, 2, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 6, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 3, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 3, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 6, 0, 0, 2, 0, 1, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0
(list; graph; listen)
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OFFSET
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1,4
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 78, Eq. (32.25).
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FORMULA
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Multiplicative with a(2^e)=3(1+(-1)^e)/2, a(3^e)=1, a(p^e)=(1+(-1)^e) if p=2 (mod 3) and a(p^e)=1+e if p=1 (mod 3).
G.f.: ((Sum_{k} x^(k^2))(Sum_{k} x^(3k^2))-1)/2.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 1/2*polcoeff(sum(k=1, sqrtint(n), 2*x^k^2, 1+x^n*O(x))*sum(k=1, sqrtint(n\3), 2*x^(3*k^2), 1+x^n*O(x)), n))
(PARI) a(n)=if(n<1, 0, qfrep([1, 0; 0, 3], n)[n]) /* Michael Somos Jun 05 2005 */
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CROSSREFS
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A033716(n)=2a(n), if n>0.
Sequence in context: A080159 A144299 A060514 this_sequence A115979 A067168 A099475
Adjacent sequences: A096933 A096934 A096935 this_sequence A096937 A096938 A096939
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Jul 15 2004
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