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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 September 11 15:28 EDT 2024. Contains 375836 sequences. (Running on oeis4.)