A077263 - OEIS

A077263

Number of (undirected) cycles in the n-th order antiprism graph.

63, 179, 523, 1619, 5239, 17379, 58323, 196691, 664623, 2247443, 7601883, 25715603, 86993639, 294295491, 995592355, 3368062355, 11394070559, 38545861491, 130399711915, 441139061715, 1492362751831, 5048627021731, 17079382870643, 57779138376659

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OFFSET

3,1

LINKS

Table of n, a(n) for n=3..26.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (6,-11,8,-3,2,-1).

FORMULA

a(n) = 6*a(n-1) - 11*a(n-2) + 8*a(n-3) - 3*a(n-4) + 2*a(n-5) - a(n-6) for n>8. - Eric W. Weisstein, Dec 19 2013

G.f.: x^3*(63 - 199*x + 142*x^2 - 54*x^3 + 35*x^4 - 19*x^5)/((1 - x)^3*(1 - 3*x - x^2 - x^3)). - Bruno Berselli, Dec 20 2013

MATHEMATICA

LinearRecurrence[{6, -11, 8, -3, 2, -1}, {63, 179, 523, 1619, 5239, 17379}, 22] (* Eric W. Weisstein, Dec 19 2013 *)

Table[4 n (n - 1) + RootSum[-1 - # - 3 #^2 + #^3 &, #^n &], {n, 3, 20}] (* Eric W. Weisstein, May 05 2017 *)

CoefficientList[Series[(63 - 199 x + 142 x^2 - 54 x^3 + 35 x^4 - 19 x^5)/((-1 + x)^3 (-1 + 3 x + x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 14 2017 *)

CROSSREFS

Cf. A077265.

Sequence in context: A330433 A044395 A044776 * A098140 A008895 A359563

Adjacent sequences: A077260 A077261 A077262 * A077264 A077265 A077266

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Nov 01 2002

EXTENSIONS

a(7)-a(10) from Max Alekseyev, May 02 2010

STATUS

approved