OFFSET
0,2
COMMENTS
The denominator is a parameterization of the Alexander polynomial for the knot 7_6. The g.f. is the image of the g.f. of A030191 under the modified Chebyshev transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2))
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-7,5,-1).
FORMULA
G.f.: -(x-1)*(x+1)*(x^2+1) / (x^4-5*x^3+7*x^2-5*x+1). - Colin Barker, Feb 10 2014
a(n) = 5*a(n-1)-7*a(n-2)+5*a(n-3)-a(n-4) for n>4. - Colin Barker, Feb 10 2014
MATHEMATICA
CoefficientList[Series[(1 - x) (x + 1) (x^2 + 1)/(x^4 -5 x^3 + 7 x^2 - 5 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
LinearRecurrence[{5, -7, 5, -1}, {1, 5, 18, 60, 197}, 30] (* Harvey P. Dale, Oct 06 2015 *)
PROG
(PARI) Vec(-(x-1)*(x+1)*(x^2+1)/(x^4-5*x^3+7*x^2-5*x+1) + O(x^100)) \\ Colin Barker, Feb 10 2014
(Magma) I:=[1, 5, 18, 60, 197, 650, 2153, 7140]; [n le 8 select I[n] else 5*Self(n-1)-7*Self(n-2)+5*Self(n-3)-Self(n-4) : n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 16 2004
EXTENSIONS
g.f. corrected by Colin Barker, Feb 10 2014
STATUS
approved