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A033718
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Product theta3(q^d); d | 5.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p 102 eq 9.
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
A. Berkovich and H. Yesilyurt, Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms
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FORMULA
| 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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PROG
| (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
| Sequence in context: A048866 A138527 A144377 * A033737 A033747 A087611
Adjacent sequences: A033715 A033716 A033717 * A033719 A033720 A033721
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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