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

Author

Eric W. Weisstein, Nov 01 2002

Keywords

• nonn
• easy

Comments

Also the number of minimal edge cuts in the n-trapezohedron graph. - Eric W. Weisstein, Dec 11 2024

Links

• Eric Weisstein's World of Mathematics, Antiprism Graph.
• Eric Weisstein's World of Mathematics, Graph Cycle.
• Eric Weisstein's World of Mathematics, Minimal Edge Cut.
• Eric Weisstein's World of Mathematics, Trapezohedral Graph.
• Index entries for linear recurrences with constant coefficients, signature (6,-11,8,-3,2,-1).

Crossrefs

Cf. A077265.

Programs

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 *)

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

Extensions

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