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A124352 Number of (directed) Hamiltonian paths on the n-antiprism graph. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 10:38 EDT 2019. Contains 322209 sequences. (Running on oeis4.)