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Search: id:A033718
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| A033718 |
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Product theta3(q^d); d | 5. |
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+0
2
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| 1, 2, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 8, 0, 0, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 6, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 10, 0, 0, 8, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 4, 0, 0
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of representations of n as a sum of five times a square and a square. - Ralf Stephan, May 14 2007
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
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LINKS
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A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms
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FORMULA
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Theta series of lattice with Gram matrix [1 0 / 0 5].
Expansion of phi(q)phi(q^5) in powers of q where phi(q) is a Ramanujan theta function.
Euler transform of period 20 sequence [ 2, -3, 2, -1, 4, -3, 2, -1, 2, -6, 2, -1, 2, -3, 4, -1, 2, -3, 2, -2, ...]. - Michael Somos Aug 13 2006
If p is prime then a(p) is nonzero iff p is in A033205.
0=a(n)a(2n) and 2*A035170(n)=a(n)+a(2n) if n>0. - Michael Somos Oct 21 2006
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PROGRAM
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(PARI) {a(n)=if(n<1, n==0, qfrep([1, 0; 0, 5], n)[n]*2)} /* Michael Somos Aug 13 2006 */
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CROSSREFS
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Sequence in context: A048866 A138527 A144377 this_sequence A033737 A033747 A087611
Adjacent sequences: A033715 A033716 A033717 this_sequence A033719 A033720 A033721
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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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