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A125510
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Theta series of 4-dimensional lattice QQF.4.g.
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1
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1, 6, 6, 42, 6, 36, 42, 48, 6, 150, 36, 72, 42, 84, 48, 252, 6, 108, 150, 120, 36, 336, 72, 144, 42, 186, 84, 474, 48, 180, 252, 192, 6, 504, 108, 288, 150, 228, 120, 588, 36, 252, 336, 264, 72, 900, 144, 288, 42, 342, 186, 756, 84, 324, 474, 432, 48, 840, 180, 360, 252, 372
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| John Cannon, Table of n, a(n) for n = 0..5000
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
| Expansion of a(x) * a(x^2) in powers of x where a() is a cubic AGM function. - Michael Somos Feb 10 2011
G.f.: 1 + 6 * (Sum_{n>0} F(x^n) + 3 * F(x^(3*n))) where F(x) = (x + x^3) / (1 - x^2)^2. - Michael Somos Feb 10 2011
G.f.: 1 + 6 * (Sum_{n>0} n * F(x^n) + (3*n) * F(x^(3*n)))) where F(x) = x / (1 + x). - Michael Somos Feb 10 2011
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EXAMPLE
| 1 + 6*x + 6*x^2 + 42*x^3 + 6*x^4 + 36*x^5 + 42*x^6 + 48*x^7 + 6*x^8 + ...
1 + 6*q^2 + 6*q^4 + 42*q^6 + 6*q^8 + 36*q^10 + 42*q^12 + 48*q^14 + 6*q^16 + ...
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PROG
| (PARI) {a(n) = if(n<1, n==0, 6 * (sumdiv( n, d, (d%2) * d) + if( n%3, 0, 3 * sumdiv( n/3, d, (d%2) * d))))} /* Michael Somos Feb 10 2011 */
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CROSSREFS
| Sequence in context: A186982 A196075 A156099 * A117859 A102901 A014435
Adjacent sequences: A125507 A125508 A125509 * A125511 A125512 A125513
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2007
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