A099846 - OEIS

%I #10 Sep 09 2015 01:25:47

%S 1,3,5,8,15,29,55,104,196,368,692,1304,2457,4627,8713,16408,30899,

%T 58189,109583,206368,388632,731872,1378264,2595552,4887953,9205011,

%U 17334909,32645160,61477479,115774605,218027143,410589480,773223548,1456137296

%N An Alexander sequence for the knot 8_5.

%C 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.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,5,-4,3,-1).

%F G.f.: 1/(1-3x+4x^2-5x^3+4x^4-3x^5+x^6).

%F 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

%t 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 *)

%Y Cf. A099854.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 27 2004