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

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