A307933 Number of (undirected) Hamiltonian paths in the n-antiprism graph.

120, 408, 1200, 3240, 8330, 20720, 50418, 120760, 285846, 670416, 1560728, 3611020, 8311110, 19042656, 43459344, 98838684, 224091320, 506660240, 1142669766, 2571214756, 5773744326, 12940614624, 28953267050, 64676245192, 144261049680, 321334401528, 714843635370, 1588357198980

Offset

3,1

Links

Table of n, a(n) for n=3..30.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Hamiltonian Path

Formula

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

Conjectures from Colin Barker, Mar 29 2020: (Start)

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).

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.

(End)

Crossrefs

Cf. A124352.

Sequence in context: A226884 A273509 A147983 * A235239 A337469 A235232

Adjacent sequences: A307930 A307931 A307932 * A307934 A307935 A307936

Keyword

nonn

Author

Eric W. Weisstein, May 06 2019

Extensions

a(30) corrected by Georg Fischer, Jan 25 2020

Status

approved