The OEIS is supported by the many generous donors to the OEIS Foundation.

A099846
An Alexander sequence for the knot 8_5.
1
1, 3, 5, 8, 15, 29, 55, 104, 196, 368, 692, 1304, 2457, 4627, 8713, 16408, 30899, 58189, 109583, 206368, 388632, 731872, 1378264, 2595552, 4887953, 9205011, 17334909, 32645160, 61477479, 115774605, 218027143, 410589480, 773223548, 1456137296
OFFSET
0,2
The g.f. is a transformation of the g.f. 1/((1-x)(1-2x-x^2)) of A048739 under the mapping G(x)->(1/(1+x^2)^3)G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial of the knot 8_5. Relates 8_5 to the Pell numbers.
FORMULA
G.f.: 1/(1-3x+4x^2-5x^3+4x^4-3x^5+x^6).
a(0)=1, a(1)=3, a(2)=5, a(3)=8, a(4)=15, a(5)=29, a(n)=3*a(n-1)- 4*a(n-2)+ 5*a(n-3)-4*a(n-4)+3*a(n-5)-a(n-6). - Harvey P. Dale, Sep 25 2011
MATHEMATICA
CoefficientList[Series[1/(1-3x+4x^2-5x^3+4x^4-3x^5+x^6), {x, 0, 40}], x] (* or *) LinearRecurrence[{3, -4, 5, -4, 3, -1}, {1, 3, 5, 8, 15, 29}, 41] (* Harvey P. Dale, Sep 25 2011 *)
CROSSREFS
Cf. A099854.
Sequence in context: A208723 A285010 A352917 * A141775 A056765 A080006
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 27 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 08:53 EDT 2024. Contains 376067 sequences. (Running on oeis4.)