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A028887
Theta series of 4-dimensional 5-modular lattice with det 25 and minimal norm 2.
5
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
OFFSET
0,2
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).
LINKS
FORMULA
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
EXAMPLE
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 + ...
MATHEMATICA
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 *)
PROG
(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 */
CROSSREFS
Sequence in context: A236864 A372566 A101527 * A283118 A274536 A051395
KEYWORD
nonn
STATUS
approved