A077263 - OEIS

%I #38 Dec 11 2024 09:26:35

%S 63,179,523,1619,5239,17379,58323,196691,664623,2247443,7601883,

%T 25715603,86993639,294295491,995592355,3368062355,11394070559,

%U 38545861491,130399711915,441139061715,1492362751831,5048627021731,17079382870643,57779138376659

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

%C Also the number of minimal edge cuts in the n-trapezohedron graph. - _Eric W. Weisstein_, Dec 11 2024

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrapezohedralGraph.html">Trapezohedral Graph</a>.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,8,-3,2,-1).

%F 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

%F 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

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

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

%t 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 *)

%Y Cf. A077265.

%K nonn,easy

%O 3,1

%A _Eric W. Weisstein_, Nov 01 2002

%E a(7)-a(10) from _Max Alekseyev_, May 02 2010