A366508 a(n) = Lucas(2*n) + 2*(-1)^n + 1.

2, 10, 17, 50, 122, 325, 842, 2210, 5777, 15130, 39602, 103685, 271442, 710650, 1860497, 4870850, 12752042, 33385285, 87403802, 228826130, 599074577, 1568397610, 4106118242, 10749957125, 28143753122, 73681302250, 192900153617, 505019158610, 1322157322202

Offset

1,1

Comments

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

Links

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

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

Cf. A005248 (bisection of the Lucas numbers).

Sequence in context: A214086 A127492 A258974 * A077247 A341032 A082939

Adjacent sequences: A366505 A366506 A366507 * A366509 A366510 A366511

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 11 2023

Status

approved