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A028887
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Theta series of 4-dimensional 5-modular lattice with det 25 and minimal norm 2.
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5
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1, 6, 18, 24, 42, 6, 72, 48, 90, 78, 18, 72, 168, 84, 144, 24, 186, 108, 234, 120, 42, 192, 216, 144, 360, 6, 252, 240, 336, 180, 72, 192, 378, 288, 324, 48, 546, 228, 360, 336, 90, 252, 576, 264, 504, 78, 432, 288, 744, 342, 18, 432, 588, 324, 720, 72, 720, 480
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OFFSET
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0,2
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).
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LINKS
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John Cannon, Table of n, a(n) for n = 0..5000
Shaun Cooper and Dongxi Ye, Level 14 AND 15 Analogues of Ramanujan's Elliptic Functions to Alternative Bases, preprint, 2015.
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
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a(n) = 6*b(n) where b(n) is multiplicative with a(0) = 1, b(5^e) = 1, b(p^e) = (p^(e+1) - 1) / (p - 1) otherwise. - Michael Somos, Feb 04 2006
G.f. 1 + 6 * (Sum_{k>0} k * x^k / (1 - x^k) - 5*k * x^(5*k) / (1 - x^(5*k))). - Michael Somos, Feb 04 2006
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EXAMPLE
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G.f. = 1 + 6*x + 18*x^2 + 24*x^3 + 42*x^4 + 6*x^5 + 72*x^6 + 48*x^7 + ...
G.f. = 1 + 6*q^2 + 18*q^4 + 24*q^6 + 42*q^8 + 6*q^10 + 72*q^12 + 48*q^14 + ...
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MATHEMATICA
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a[ n_] := If[ n < 1, Boole[ n == 0], 6 Sum[ If[ Mod[ d, 5] > 0, d, 0], {d, Divisors @ n }]]; (* Michael Somos, Jun 12 2014 *)
a[ n_] := SeriesCoefficient[ 1 + 6 Sum[ k x^k / (1 - x^k) - 5 k x^(5 k) / (1 - x^(5 k)), {k, n}], {x, 0, n}]; (* Michael Somos, Jun 12 2014 *)
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PROG
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(PARI) {a(n) = if( n<1, n==0, 6 * sumdiv(n, d, (d%5>0) * d))}; /* Michael Somos, Feb 04 2006 */
(PARI) {a(n) = my(G); if( n<0, 0, G = [ 2, 1, 0, 0; 1, 2, 1, 0; 0, 1, 4, 5; 0, 0, 5, 10]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* Michael Somos, Jun 12 2014 */
(Sage) ModularForms( Gamma0(5), 2, prec=70).0; # Michael Somos, Jun 12 2014
(MAGMA) Basis( ModularForms( Gamma0(5), 2), 70) [1]; /* Michael Somos, Jun 12 2014 */
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CROSSREFS
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Sequence in context: A015707 A236864 A101527 * A283118 A274536 A051395
Adjacent sequences: A028884 A028885 A028886 * A028888 A028889 A028890
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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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STATUS
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approved
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