|
| |
|
|
A028572
|
|
Expansion of theta_3(z)*theta_3(2z)+theta_2(z)*theta_2(2z) in powers of q^(1/4).
|
|
0
| |
|
|
1, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 6, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 2, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
|
|
|
LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
| Expansion of phi(q^4)*phi(q^8) +4*q^3*psi(q^8)*psi(q^16) in powers of q where phi(),psi() are Ramanujan theta functions.
G.f.: Sum_{n,m} x^(3*(n^2+m^2)+2*n*m) . - Michael Somos Nov 20 2006 */
|
|
|
EXAMPLE
| 1 + 4*q^(3/4) +2*q +2*q^2 +4*q^(11/4) +4*q^3 +2*q^4 + 4*q^(19/4) +4*q^6 + ...
|
|
|
PROG
| (PARI) {a(n)=if(n<1, n==0, qfrep([3, 1; 1, 3], n)[n]*2)} /* Michael Somos Nov 20 2006 */
|
|
|
CROSSREFS
| Sequence in context: A056582 A167891 A105087 * A107492 A159257 A107088
Adjacent sequences: A028569 A028570 A028571 * A028573 A028574 A028575
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
