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 A028959 Theta series of quadratic form with Gram matrix [ 2, 1; 1, 12 ]. 11
 1, 2, 0, 0, 2, 0, 4, 0, 4, 2, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 4, 2, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 0, 0, 4, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 4, 0, 8, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS theta[2,1;1,2d](z)=theta_3(z)*theta_3((4d-1)z)+theta_2(z)*theta_2((4d-1)z), generalizing the formula for theta(A_2), which is the case d=1 - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 16 2000. The number of integer solutions (x, y) to x^2 + x*y + 6*y^2 = n, discriminant -23. - Ray Chandler, Jul 12 2014 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). REFERENCES Köklüce, Bülent. "Cusp forms in S_6 (Gamma_ 0(23)), S_8 (Gamma_0 (23)) and the number of representations of numbers by some quadratic forms in 12 and 16 variables." The Ramanujan Journal 34.2 (2014): 187-208. See F_1, p. 195. LINKS John Cannon, Table of n, a(n) for n = 0..5000 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of phi(x) * phi(x^23) + 4*x^6 * psi(x^2) * psi(x^46) in powers of x where phi(), psi() are Ramanujan theta functions. - Michael Somos, Mar 28 2015 G.f. is a period 1 Fourier series which satisfies f(-1 / (23 t)) = 23^(1/2) (t/i) f(t) where q = exp(2 Pi i t). - Michael Somos, Mar 28 2015 G.f.: (theta_3(z)*theta_3(23z) + theta_2(z)*theta_2(23z)). EXAMPLE G.f. = 1 + 2*x + 2*x^4 + 4*x^6 + 4*x^8 + 2*x^9 + 4*x^12 + 2*x^16 + 4*x^18 + ... G.f. = 1 + 2*q^2 + 2*q^8 + 4*q^12 + 4*q^16 + 2*q^18 + 4*q^24 + 2*q^32 + 4*q^36 + 2*q^46 + 4*q^48 + 2*q^50 + 4*q^52 + 4*q^54 + 4*q^64 + 6*q^72 + 4*q^78 + 8*q^96 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x] EllipticTheta[ 3, 0, x^23] + EllipticTheta[ 2, 0, x] EllipticTheta[ 2, 0, x^23], {x, 0, n}]; (* Michael Somos, Mar 28 2015 *) CROSSREFS Cf. A028958. Sequence in context: A334596 A291900 A263146 * A317642 A258762 A079181 Adjacent sequences:  A028956 A028957 A028958 * A028960 A028961 A028962 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)