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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i). LINKS 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 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: A015707 A236864 A101527 * A283118 A274536 A051395 Adjacent sequences:  A028884 A028885 A028886 * A028888 A028889 A028890 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 17 16:12 EDT 2021. Contains 343063 sequences. (Running on oeis4.)