|
| |
|
|
A113946
|
|
Series expansion of Farey rational polynomial based on A112627.
|
|
0
|
|
|
|
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;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
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.
|
|
|
LINKS
|
Table of n, a(n) for n=0..23.
Index to sequences with linear recurrences with constant coefficients, signature (-1,16,16).
|
|
|
FORMULA
|
b(n)=coefficient series expansion of (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-16/9)*b(n)
a(n) = (5*(-4)^n+4*(-1)^n+81*4^n)/60 for n>0. G.f.: -(2*x+1)^3 / ((x+1)*(4*x-1)*(4*x+1)). [Colin Barker, Dec 03 2012]
|
|
|
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: A211809 A211922 A139209 * A193696 A147359 A034447
Adjacent sequences: A113943 A113944 A113945 * A113947 A113948 A113949
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Roger L. Bagula, Jan 31 2006
|
|
|
STATUS
|
approved
|
| |
|
|
