OFFSET
0,2
COMMENTS
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-4,5,-4,3,-1).
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 27 2004
STATUS
approved