|
Search: id:A138806
|
|
|
| A138806 |
|
Expansion of (theta_3(q) * theta_3(q^27) + theta_2(q) * theta_2(q^27) - 1) / 2 in powers of q. |
|
+0
2
|
|
| 1, 0, 0, 1, 0, 0, 2, 0, 3, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0, 0, 2, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
1,7
|
|
|
FORMULA
|
a(n) is multiplicative and a(3^e) = 3 if e>1, a(p^e) = e+1 if p == 1 (mod 6), a(p^e) = (1 + (-1)^e) / 2 if p == 5 (mod 6).
a(3*n + 2) = a(4*n + 2) = 0.
G.f.: (Sum_{i,j} x^(i*i + i*j + 7*j*j) - 1) / 2.
|
|
EXAMPLE
|
q + q^4 + 2*q^7 + 3*q^9 + 2*q^13 + q^16 + 2*q^19 + q^25 + 3*q^27 + ...
|
|
PROGRAM
|
(PARI) {a(n) = if( n<1, 0, if( n%3 == 2, 0, if( n%3==1, sumdiv(n, d, kronecker(-3, d)), if( n%9==0, 3 * sumdiv(n/9, d, kronecker(-3, d))))))}
(PARI) {a(n) = if( n<1, 0, sumdiv(n, d, kronecker(-3, d)) - if( n%3==0, sumdiv(n/3, d, [0, 1, -1, -3, 1, -1, 3, 1, -1][d%9+1])))}
(PARI) {a(n) = if( n<1, 0, qfrep([2, 1; 1, 14], n, 1)[n])}
|
|
CROSSREFS
|
A138805(n) = 2 * a(n) unless n=0. A033687(n) = a(3*n + 1). A097195(n) = a(6*n + 1). A123884(n) = a(12*n + 1). 2 * A121361(n) = a(12*n + 7).
Sequence in context: A080300 A116864 A079302 this_sequence A142971 A104117 A114511
Adjacent sequences: A138803 A138804 A138805 this_sequence A138807 A138808 A138809
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
Michael Somos, Mar 30 2008
|
|
|
Search completed in 0.005 seconds
|
