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

3,1

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

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

Crossrefs

Cf. A124353 (numbers of directed Hamiltonian cycles).

Sequence in context: A202196 A060663 A092000 * A158562 A234728 A234721

Adjacent sequences: A124349 A124350 A124351 * A124353 A124354 A124355

Keyword

nonn

Author

Eric W. Weisstein, Oct 27 2006

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

Status

approved