A124352 Number of directed Hamiltonian paths on the n-antiprism graph.

240, 816, 2400, 6480, 16660, 41440, 100836, 241520, 571692, 1340832, 3121456, 7222040, 16622220, 38085312, 86918688, 197677368, 448182640, 1013320480, 2285339532, 5142429512, 11547488652, 25881229248, 57906534100, 129352490384, 288522099360, 642668803056, 1429687270740, 3176714397960

Offset: 3

Author

Eric W. Weisstein, Oct 27 2006

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..50
• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Hamiltonian Path

Crossrefs

Cf. A124353 (numbers of directed Hamiltonian cycles).

Formula

Conjectures from Colin Barker, Dec 21 2015: (Start)

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.

G.f.: 4*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).

(End)

Equivalent conjecture: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) +672*n -1376 -72*n^2 if n>=9. - R. J. Mathar, Jan 25 2016

Extensions

a(6)-a(10) from Eric W. Weisstein, Apr 03 2008

a(11)-a(18) from Eric W. Weisstein, Dec 16 2013

a(19)-a(30) from Andrew Howroyd, Dec 20 2015