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A294152 Chromatic invariant of the n-antiprism graph. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)