|
Search: id:A113946
|
|
|
| A113946 |
|
Series expansion of Farey rational polynomial based on A112627. |
|
+0
1
|
|
| 1, 5, 23, 81, 367, 1297, 5871, 20753, 93935, 332049, 1502959, 5312785, 24047343, 85004561, 384757487, 1360072977, 6156119791, 21761167633, 98497916655, 348178682129, 1575966666479, 5570858914065, 25215466663663, 89133742625041
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Polynomial expanded is constant*(x+1/2)^2*(1+2x)/(1-x-16x^2+16x^3) the Jasinski rational polynomial p[x_] = (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) f[x_] := 1/p[x] /; 0 <= x <= 1/2 f[x_] := p[x] /; 1/2 < x <= 1 gives a Farey like function with maximum at 1.
|
|
FORMULA
|
b(n)=coeficient series expansion of (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-16/9)*b(n)
|
|
MATHEMATICA
|
b = -(16/9)*ReplacePart[Table[Coefficient[Series[(9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, 0, 30}], -9/16, 1]
|
|
CROSSREFS
|
Cf. A112627.
Sequence in context: A121868 A111584 A139209 this_sequence A034447 A121329 A146013
Adjacent sequences: A113943 A113944 A113945 this_sequence A113947 A113948 A113949
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2006
|
|
|
Search completed in 0.002 seconds
|
