OFFSET
0,2
COMMENTS
This counts independent sets in certain graphs.
LINKS
S. Kitaev and A. Burstein, Counting independent sets on path-schemes Journal of Integer Sequences 9, no. 2 (2006), Article 06.2.2
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,1).
EXAMPLE
For n=4, a(4)=7 because the graph is a cycle, and the independent sets are the empty set, {1}, {2}, {3}, {4}, {1,3} and {2,4}.
MATHEMATICA
CoefficientList[Series[(1+x+x^3+x^5)/( (1-x^2+x^3)*(1-x-x^3) ), {x, 0, 40}], x] (* Vaclav Kotesovec, Aug 25 2014 *)
LinearRecurrence[{1, 1, -1, 1, -1, 1}, {1, 2, 3, 5, 7, 11}, 50] (* Harvey P. Dale, Sep 22 2024 *)
PROG
(PARI) Vec((1+x+x^3+x^5)/((1-x^2+x^3)*(1-x-x^3)) + O(x^50)) \\ Michel Marcus, May 24 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Signy Olafsdottir (signy06(AT)ru.is), May 09 2010
EXTENSIONS
Edited by N. J. A. Sloane, May 18 2010
More terms from Vaclav Kotesovec, Aug 25 2014
STATUS
approved