The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008444 Theta series of A_4 lattice. 5
 1, 20, 30, 60, 60, 120, 40, 180, 150, 140, 130, 240, 180, 360, 120, 260, 220, 480, 210, 400, 360, 240, 360, 660, 200, 620, 240, 600, 540, 600, 240, 640, 630, 720, 320, 780, 420, 1080, 600, 480, 650, 840, 360, 1260, 720, 840, 440, 1380, 660, 860, 630, 640, 1080, 1560, 400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). REFERENCES J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110. LINKS John Cannon, Table of n, a(n) for n = 0..5000 G. Nebe and N. J. A. Sloane, Home page for this lattice Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of f(-x)^5 / f(-x^5) + 25 * x * f(-x^5)^5 / f(-x) in powers of x where f() is a Ramanujan theta function. - Michael Somos, Feb 06 2011 Expansion of (1 / Pi) integral_{0 .. Pi/2} theta_3(z, q)^5 + theta_4(z, q)^5 dz in powers of q^2. - Michael Somos, Jan 01 2012 Coefficient of x^0 in the expansion f(x * q, q / x)^5 in powers of q^2 where f() is a Ramanujan theta function. - Michael Somos, Jan 01 2012 G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 5^(3/2) (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A023916. - Michael Somos, Feb 06 2011 A023916(5*n) = a(n) for all n in Z. EXAMPLE G.f. = 1 + 20*x + 30*x^2 + 60*x^3 + 60*x^4 + 120*x^5 + 40*x^6 + 180*x^7 + ... G.f. = 1 + 20*q^2 + 30*q^4 + 60*q^6 + 60*q^8 + 120*q^10 + 40*q^12 + 180*q^14 + 150*q^16 + 140*q^18 + 130*q^20 + 240*q^22 + 180*q^24 + 360*q^26 + 120*q^28 + 260*q^30 + 220*q^32 + 480*q^34 + 210*q^36 + 400*q^38 + 360*q^40 + 240*q^42 + 360*q^44 + 660*q^46 + 200*q^48 + 620*q^50 + ... MATHEMATICA a[ n_] := With[ {u1 = QPochhammer[ x], u5 = QPochhammer[ x^5]}, SeriesCoefficient[ u1^5/u5 + 25 x u5^5/u1, {x, 0, n}]]; (* Michael Somos, Nov 13 2014 *) terms = 55; f[q_] = LatticeData["A4", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; CoefficientList[s, q^2][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *) PROG (MAGMA) L := Lattice("A", 4); A := ThetaSeries(L, 120); A; (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^5 / eta(x^5 + A) + 25 * x * eta(x^5 + A)^5 / eta(x + A), n))}; /* Michael Somos, Feb 06 2011 */ (MAGMA) A := Basis( ModularForms( Gamma1(5), 2), 55) ; A[1] + 20*A[2] + 30*A[3]; /* Michael Somos, Nov 13 2014 */ CROSSREFS Cf. A000007, A000122, A004016, A004015, A008445, A008446, A008447, A008448, A008449 (Theta series of lattices A_0, A_1, A_2, A_3, A_5,...) Sequence in context: A066027 A256227 A142342 * A268984 A066214 A285494 Adjacent sequences:  A008441 A008442 A008443 * A008445 A008446 A008447 KEYWORD nonn,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)