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Search: id:A089802
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| A089802 |
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Expansion of Jacobi theta function (theta_4(q^3)-theta_4(q^(1/3)))/2/q^(1/3). |
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+0
3
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| 1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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I. J. Zucker, "Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums." J. Phys. A: Math. Gen. 23, 117-132, 1990.
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LINKS
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Eric Weisstein's World of Mathematics, Jacobi Theta Functions
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FORMULA
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Expansion of q^(-1/3)*(eta(q)*eta(q^6)^2)/(eta(q^2)*eta(q^3)) in powers of q. - Michael Somos Apr 12 2005
Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, -1, ...]. - Michael Somos, Apr 12 2005
|a(n)| is the characteristic function of A001082. - Michael Somos Oct 31 2005
G.f.: Sum_{k} (-1)^k x^((3k^2-2*k)/2) = Product_{k>0} (1-x^(6k))(1-x^(6k-1))(1-x^(6k-5)) . - Michael Somos Oct 31 2005
A002448(3n+1)=-2*a(n). - Michael Somos Jul 07 2006
Expansion of f(-x, -x^5) in powers of x, where f(a, b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
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PROGRAM
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(PARI) a(n)=(-1)^n*issquare(3*n+1) /* Michael Somos Apr 12 2005 */
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CROSSREFS
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a(n)=(-1)^n*A089801(n).
Sequence in context: A094875 A012245 A089801 this_sequence A015274 A011651 A016264
Adjacent sequences: A089799 A089800 A089801 this_sequence A089803 A089804 A089805
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KEYWORD
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sign
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Nov 12, 2003
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EXTENSIONS
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Corrected by njas, Nov 05 2005
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