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

Author

Eric W. Weisstein, May 06 2019

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Hamiltonian Path

Crossrefs

Cf. A124352.

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)

Extensions

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