A366511 a(n) = Lucas(2*n) + 2^(n + 1) + 1.

8, 16, 35, 80, 188, 451, 1100, 2720, 6803, 17176, 43700, 111875, 287828, 743416, 1926035, 5001920, 13014188, 33909571, 88452380, 230923280, 603268883, 1576786216, 4122895460, 10783511555, 28210861988, 73815519976, 193168589075, 505556029520, 1323231064028

Offset

1,1

Comments

For n >= 3, the number of independent vertex sets in the n-trapezohedron graph.

Links

Table of n, a(n) for n=1..29.

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

Cf. A005248 (bisection of the Lucas numbers).

Sequence in context: A072578 A271994 A058516 * A217672 A194601 A200271

Adjacent sequences: A366508 A366509 A366510 * A366512 A366513 A366514

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 11 2023

Status

approved