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A002519
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Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.
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3
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1, 0, 0, 1728, 106472, 1734912, 19335168, 141575552, 805208040, 3725209088, 14647517184, 50579062848, 156715230240, 443680116992, 1162915024896, 2851005884544, 6596700471272, 14509559545344, 30507866603520
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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R. Bacher and B. B. Venkov, Reseaux entiers unimodulaires sans racine en dimension 27 et 28, in Reseaux euclidiens, designs spheriques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
R. Bacher and B. B. Venkov, Reseaux entiers unimodulaires sans racine en dimension 27 et 28 (html, ps).
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FORMULA
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t3^28-56*t3^20*D8+280*t3^12*D8^2-512*t3^4*D8^3 where t3=theta3(z) and D8=(theta2(z)theta4(z))^4/16
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MATHEMATICA
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terms = 19; t2 = EllipticTheta[2, 0, z]; t3 = EllipticTheta[3, 0, z]; t4 = EllipticTheta[4, 0, z]; D8 = (t2*t4)^4/16; s = t3^28 - 56*t3^20*D8 + 280*t3^12*D8^2 - 512*t3^4*D8^3 + O[z]^terms; CoefficientList[s, z] (* Jean-François Alcover, Jul 06 2017 *)
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CROSSREFS
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Cf. A002520.
Sequence in context: A017523 A237490 A223324 * A052068 A289210 A289209
Adjacent sequences: A002516 A002517 A002518 * A002520 A002521 A002522
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 04 2000
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STATUS
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approved
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