|
Search: id:A111165
|
|
|
| A111165 |
|
Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q,q^3)/qf(q^2,q^3). |
|
+0
2
|
|
| 1, -1, 1, -1, 0, 1, -1, 0, 1, -2, 2, 0, -2, 2, -1, -1, 3, -2, -1, 3, -3, 0, 4, -5, 2, 3, -6, 4, 2, -7, 6, 0, -7, 9, -2, -7, 10, -5, -6, 13, -8, -5, 15, -13, -1, 16, -17, 2, 16, -22, 8, 16, -27, 14, 12, -30, 22, 9, -34, 29, 3, -36, 39, -5, -37, 47, -14, -36, 58, -26, -33, 66, -41, -26, 75, -56, -18, 81, -74, -4, 87, -94, 12, 87, -113, 34
(list; graph; listen)
|
|
|
OFFSET
|
0,10
|
|
|
FORMULA
|
Euler transform of period 3 sequence [ -1, 1, 0, ...]. - Michael Somos Dec 23 2007
G.f.: Product_{k>=0} (1 - x^(3*k+1)) / (1 - x^(3*k+2)).
|
|
PROGRAM
|
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=0, n\3, (1 - x^(3*k+1)) / (1 - x^(3*k+2)), 1 + x * O(x^n)), n))} /* Michael Somos Dec 23 2007 */
|
|
CROSSREFS
|
Cf. A111375. Convolution inverse of A111317.
Sequence in context: A109265 A035668 A066518 this_sequence A029321 A029310 A134131
Adjacent sequences: A111162 A111163 A111164 this_sequence A111166 A111167 A111168
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
njas, Nov 09 2005
|
|
|
Search completed in 0.002 seconds
|
