A294152 Chromatic invariant of the n-antiprism graph.

0, 2, 11, 38, 112, 309, 828, 2190, 5759, 15106, 39580, 103657, 271416, 710618, 1860467, 4870814, 12752008, 33385245, 87403764, 228826086, 599074535, 1568397562, 4106118196, 10749957073, 28143753072, 73681302194, 192900153563, 505019158550, 1322157322144

Offset

1,2

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Chromatic Invariant

Index entries for linear recurrences with constant coefficients, signature (5, -8, 5, -1).

Formula

a(n) = A005248(n) - 2*n - 1.

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

a(n) = 5*a(n-1) - 8*a(n-2) + 5*a(n-3) - a(n-4).

G.f.: x^2*(2 + x - x^2)/((-1 + x)^2*(1 - 3*x + x^2)).

a(n) = -1 + ((3-sqrt(5))/2)^n + ((3+sqrt(5))/2)^n - 2*n. - Colin Barker, Nov 16 2017

Mathematica

Table[LucasL[2 n] - 2 n - 1, {n, 3, 20}]
LinearRecurrence[{5, -8, 5, -1}, {0, 2, 11, 38}, 20]
CoefficientList[Series[(x (2 + x - x^2))/((-1 + x)^2 (1 - 3 x + x^2)), {x, 0, 20}], x]

Prog

(PARI) concat(0, Vec(x^2*(2 + x - x^2)/((-1 + x)^2*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Nov 16 2017

Crossrefs

Cf. A005248 (lucasl(2*n)).

Sequence in context: A097651 A320540 A059673 * A196701 A196850 A203534

Adjacent sequences: A294149 A294150 A294151 * A294153 A294154 A294155

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 16 2017

Status

approved