OFFSET
3,4
COMMENTS
From Alexander Adamchuk, Nov 16 2009: (Start)
For n>1 a(2n+1) = 2^(n-1) - 1 = A000225(n-1).
For n>1 a(4n) = a(4n+1) - 1 = 2^(2n-1) - 2.
For n>0 a(4n+2) = a(4n+3) = 2^(2n) - 1. (End)
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 3..1000
A. Stoimenow, Generating Functions, Fibonacci Numbers and Rational Knots, Journal of Algebra, 310 (2007), 491-525; arXiv:math/0210174 [math.GT], 2002.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1,0,-2).
FORMULA
G.f.: x^3*(1+x-x^2+x^3-x^5+2*x^6+2*x^7) / ((1-x)*(1+x)*(1+x^2)*(1-2*x^2)).
a(n) = 2*a(n-2)+a(n-4)-2*a(n-6) for n>10. - Colin Barker, Dec 26 2015
MATHEMATICA
CoefficientList[Series[(2 x^7 + 2 x^6 - x^5 + x^3 - x^2 + x + 1) / ((x-1) (x+1) (x^2+1) (2 x^2-1)), {x, 0, 50}], x] (* Vincenzo Librandi, May 17 2013 *)
PROG
(PARI) Vec(x^3*(1+x-x^2+x^3-x^5+2*x^6+2*x^7)/((1-x)*(1+x)*(1+x^2)*(1-2*x^2)) + O(x^60)) \\ Colin Barker, Dec 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Jan 03 2003
STATUS
approved