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Search: id:A028930
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| A028930 |
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Theta series of quadratic form (or lattice) with Gram matrix [ 4, 1; 1, 6 ]. |
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+0
2
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| 1, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 4, 0, 0, 0, 6, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 6, 0, 2, 0, 4, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 8, 2, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 8, 0, 2, 0, 2, 0, 0, 0, 6
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The number of integer solutions to 2x^2+xy+3y^2=n. - Michael Somos Oct 18 2005
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LINKS
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John Cannon, Table of n, a(n) for n = 0..5000
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EXAMPLE
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For n=24 the solutions are [2,2],[3,-2],[3,1] and their negatives, so a(24)=6.
1 + 2*q^4 + 2*q^6 + 2*q^8 + 2*q^12 + 2*q^16 + 2*q^18 + 4*q^24 + 2*q^26 + 4*q^32 + 4*q^36 + 6*q^48 + 2*q^52 + 2*q^54 + 2*q^58 + 2*q^62 + 4*q^64 + 6*q^72 + ...
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PROGRAM
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(PARI) a(n)=if(n<1, n==0, 2*qfrep([4, 1; 1, 6], n, 1)[n]) /* Michael Somos Oct 18 2005 */
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CROSSREFS
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Cf. A106867.
Sequence in context: A056557 A082900 A133625 this_sequence A112792 A138319 A002100
Adjacent sequences: A028927 A028928 A028929 this_sequence A028931 A028932 A028933
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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