1,5

The n X n fiveleaper graph is connected for n >=8 and traceable from n = 8 up to at least n = 29, meaning a(n) = n^2 - 1 for a(n) with 8 <= n <= 29 (and probably all larger n).

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Fiveleaper Graph

Eric Weisstein's World of Mathematics, Longest Path

Conjectures from Colin Barker, Jun 14 2019: (Start)

G.f.: x^5*(2 + 13*x - 4*x^2 - 23*x^3 + 13*x^4 + x^5) / (1 - x)^3.

a(n) = n^2 - 1 for n>7.

(End)

Cf. A307553 (number of longest paths).

Sequence in context: A109946 A141067 A296251 * A031911 A136685 A226489

Adjacent sequences: A307551 A307552 A307553 * A307555 A307556 A307557

nonn,more

Eric W. Weisstein, Apr 14 2019

approved