OFFSET
1,1
COMMENTS
For n >= 3, the number of independent vertex sets in the n-trapezohedron graph.
LINKS
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Trapezohedral Graph
Index entries for linear recurrences with constant coefficients, signature (6,-12,9,-2).
FORMULA
a(n) = 6*a(n-1) - 12*a(n-2) + 9*a(n-3) - 2*a(n-4).
G.f.: x*(8-32*x+35*x^2-10*x^3)/((1-x)*(1-2*x)*(1-3*x+x^2)).
MATHEMATICA
Table[LucasL[2 n] + 2^(n + 1) + 1, {n, 20}]
LinearRecurrence[{6, -12, 9, -2}, {8, 16, 35, 80}, 20]
CoefficientList[Series[(8 - 32 x + 35 x^2 - 10 x^3)/(1 - 6 x + 12 x^2 - 9 x^3 + 2 x^4), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 11 2023
STATUS
approved