OFFSET
1,1
COMMENTS
For n >=3, number of independent vertex sets in the n-double cone graph.
LINKS
Eric Weisstein's World of Mathematics, Double Cone Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).
FORMULA
a(n) = 3*a(n-1)-3*a(n-3)+a(n-4).
G.f.: x*(-2-4*x+13*x^2-5*x^3)/((x+1)*(x-1)*(x^2-3*x+1)).
MATHEMATICA
Table[LucasL[2 n] + 2 (-1)^n + 1, {n, 20}]
LinearRecurrence[{3, 0, -3, 1}, {2, 10, 17, 50}, 20]
CoefficientList[Series[(-2 - 4 x + 13 x^2 - 5 x^3)/(-1 + 3 x - 3 x^3 + x^4), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 11 2023
STATUS
approved