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Number of (undirected) Hamiltonian paths in the n-antiprism graph.
0

%I #13 Mar 29 2020 17:15:12

%S 120,408,1200,3240,8330,20720,50418,120760,285846,670416,1560728,

%T 3611020,8311110,19042656,43459344,98838684,224091320,506660240,

%U 1142669766,2571214756,5773744326,12940614624,28953267050,64676245192,144261049680,321334401528,714843635370,1588357198980

%N Number of (undirected) Hamiltonian paths in the n-antiprism graph.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%F a(n) = A124352(n)/2.

%F Conjectures from _Colin Barker_, Mar 29 2020: (Start)

%F G.f.: 2*x^3*(60 - 96*x - 60*x^2 + 84*x^3 + 61*x^4 - 73*x^5 - 41*x^6 + 15*x^7 + 14*x^8) / ((1 - x)^3*(1 - x - 2*x^2 - x^3)^2).

%F a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 7*a(n-4) + 5*a(n-5) - 5*a(n-6) - 3*a(n-7) + a(n-8) + a(n-9) for n>11.

%F (End)

%Y Cf. A124352.

%K nonn

%O 3,1

%A _Eric W. Weisstein_, May 06 2019

%E a(30) corrected by _Georg Fischer_, Jan 25 2020