A014584 Number of Hamiltonian paths in a 5 X n grid starting at the lower left corner and finishing in the upper right corner.

0, 1, 1, 8, 20, 104, 378, 1670, 6706, 28417, 117204, 490865, 2039569, 8512474, 35444636, 147780722, 615715196, 2566325356, 10694300534, 44570089963, 185740837148, 774080813649, 3225945847829, 13444117980220, 56028001091944, 233495908297044, 973089296878098, 4055332929187618, 16900521902518438

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The difference between A014584 and A014585 needs to be clarified. - N. J. A. Sloane, Feb 08 2013

The difference is that this sequence counts Hamiltonian paths that start in the lower left corner and end in the upper right. A014585 counts Hamiltonian paths that start in the lower left and finish in the lower right. - Ruben Zilibowitz, Jul 05 2015

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• K. L. Collins and L. B. Krompart, The number of Hamiltonian paths in a rectangular grid, Discrete Math. 169 (1997), 29-38.
• Index entries for sequences related to graphs, Hamiltonian

Crossrefs

Row n=5 of A333580.

Cf. A014585.

Formula

The reference gives a generating function.

Extensions

Definition clarified by Ruben Zilibowitz, Jul 05 2015

a(24)-a(28) from Seiichi Manyama, Mar 27 2020