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Search: id:A002706
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| A002706 |
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Theta series of 6-dimensional lattice A_6^(2) (also called LAMBDA_{3,lambda}, P_6^(5), phi_6, F_14). |
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+0
3
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| 1, 0, 42, 56, 84, 168, 280, 336, 462, 336, 840, 672, 1176, 1176, 1386, 1008, 1848, 2016, 2058, 2520, 3528, 2408, 3108, 2688, 4760, 3024, 5880, 4592, 6468, 4704, 5040, 6720, 6930, 6832, 10080, 7224, 7812, 7392, 12600, 7056, 14280, 11760, 12040, 9408
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. H. Conway and N. J. A. Sloane, Complex and integral laminated lattices, Trans. Amer. Math. Soc., 280 (1983), 463-490.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Intro. to 3rd ed.
N. Elkies, The Klein quartic in number theory, pp. 51-101 of S. Levy, ed., The Eightfold Way, Cambridge Univ. Press, 1999. MR1722413 (2001a:11103)
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LINKS
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G. Nebe and N. J. A. Sloane, Home page for this lattice
N. Elkies, The Klein quartic in number theory
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FORMULA
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A002653 - 6*A002656.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w) is a homogenous degree 6 polynomial with 28 terms. - Michael Somos Jun 03 2005
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PROGRAM
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(PARI) {a(n)=local(A, t1, t2, t3); if(n<1, n==0, A=x*O(x^n); t1=x*(eta(x+A)*eta(x^7+A))^3; t2=sum(k=1, (sqrtint(4*n+1)+1)\2, 2*x^(k*k-k), A); t3=sum(k=1, sqrtint(n), 2*x^(k*k), 1+A); A=x*O(x^(n\7)); polcoeff( (t3*subst(t3+A, x, x^7)+x^2*t2*subst(t2+A, x, x^7))^3 -6*t1, n))} /* Michael Somos Jun 03 2005 */
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CROSSREFS
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Sequence in context: A039313 A043916 A124656 this_sequence A080971 A039384 A043207
Adjacent sequences: A002703 A002704 A002705 this_sequence A002707 A002708 A002709
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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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