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Search: id:A105673
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| A105673 |
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One-half of theta series of square lattice (or half the number of ways of writing n > 0 as a sum of 2 squares), without the constant term, which is 1/2. |
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+0
2
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| 2, 2, 0, 2, 4, 0, 0, 2, 2, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 6, 4, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 2, 6, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 8, 0, 0, 4, 0, 0, 0, 2, 4, 4, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is the elliptic function K/pi - see Fine.
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; Eq. (34.4).
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FORMULA
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G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=(u-v)^2-(v-w)(4w+2). - Michael Somos May 13 2005
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EXAMPLE
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K/pi = 1/2 + 2*q + 2*q^2 + 2*q^4 + 4*q^5 + 2*q^8 + 2*q^9 + 4*q^10 + 4*q^13 + 2*q^16 + ...
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PROGRAM
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(PARI) qfrep([1, 0; 0, 1], 100)
(PARI) a(n)=if(n<1, 0, qfrep([1, 0; 0, 1], n)[n]) /* Michael Somos May 13 2005 */
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CROSSREFS
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(Theta_3)^2 is given in A004018.
Equals A004018(n)/2 for n > 0.
Adjacent sequences: A105670 A105671 A105672 this_sequence A105674 A105675 A105676
Sequence in context: A072738 A141058 A102706 this_sequence A074823 A006462 A008281
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KEYWORD
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nonn
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AUTHOR
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njas, May 05 2005
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