0,2

One of Ramanujan's 54 universal quaternary quadratic forms. - Michael Somos Apr 01 2008

B. C. Berndt, Ramanujan's Notebooks Part V, Springer-Verlag, see p. 373 Entry 31.

N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 78, Eq. (32.29).

S. Ramanujan, Collected Papers, Chap. 20, Cambridge Univ. Press 1927 (Proceedings of the Camb. Phil. Soc., 19 (1917) 11-21)

Y. Mimura, Almost Universal Quadratic Forms.

Euler transform of period 8 sequence [4, -2, 4, -8, 4, -2, 4, -4, ...]. - Michael Somos, Sep 17 2004

Multiplicative with a(n)=4b(n), b(2)=2, b(2^e)=6 if e>1, b(p^e)=(p^(e+1)-1)/(p-1) if p>2. - Michael Somos, Sep 17 2004

G.f.: 1+Sum_{k>0} 8*x^(4k)/(1+x^(4k))^2 +4*x^(2k-1)/(1-x^(2k-1))^2 = 1+Sum_{k>0} (2+(-1)^k)4k x^(2k)/(1+x^(2k)) +4(2k-1)x^(2k-1)/(1-x^(2k-1)) . - Michael Somos Oct 22 2005

Expansion of (eta(q^2)eta(q^4))^6/(eta(q)eta(q^8))^4 in powers of q.

G.f.: (theta_3(q)theta_3(q^2))^2.

G.f.: Product_{k>0} ((1-x^(2k))(1-x^(4k)))^6/((1-x^k)(1-x^(8k)))^4.

(PARI) a(n)= local(t); if(n<1, n>=0, t=2^valuation(n, 2); 4*sigma(n/t)*if(t>2, 6, t)) /* Michael Somos, Sep 17 2004 */

(PARI) a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^4+A))^6/(eta(x+A)*eta(x^8+A))^4, n)) /* Michael Somos, Sep 17 2004 */

(PARI) a(n)=if(n<1, n==0, 2*qfrep([1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 2, 0; 0, 0, 0, 2], n)[n]) /* Michael Somos Oct 29 2005 */

Sequence in context: A036302 A032377 A133690 this_sequence A160746 A160740 A046059

Adjacent sequences: A097054 A097055 A097056 this_sequence A097058 A097059 A097060

nonn

N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2004