A307554 Longest path length in the n X n fiveleaper graph.

0, 0, 0, 0, 2, 19, 47, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, 624, 675, 728, 783, 840

Offset

1,5

Comments

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).

Links

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

Formula

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)

Crossrefs

Cf. A307553 (number of longest paths).

Sequence in context: A109946 A141067 A296251 * A031911 A136685 A226489

Adjacent sequences: A307551 A307552 A307553 * A307555 A307556 A307557

Keyword

nonn,more

Author

Eric W. Weisstein, Apr 14 2019

Status

approved