A238115 Number of states arising in matrix method for enumerating Hamiltonian cycles on a 2n X 2n grid.

1, 6, 32, 182, 1117, 7280, 49625, 349998, 2535077, 18758264, 141254654, 1079364104, 8350678169, 65298467486, 515349097712, 4100346740510, 32858696386765, 265001681344568, 2149447880547398, 17524254766905368, 143540915998174577, 1180736721910617182

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv preprint arXiv:1402.0545 [math.CO], 2014.

Formula

From Andrew Howroyd, Dec 13 2024: (Start)

a(n) = Sum_{k=1..n} binomial(n,k)^2 * A000108(k).

a(n) = A086618(n) - 1. (End)

Maple

a := n -> hypergeom([1/2, -n, -n], [1, 2], 4) - 1:
seq(simplify(a(n)), n = 1..22);  # Peter Luschny, Dec 13 2024

Prog

(PARI) a(n)=sum(k=1, n, binomial(n, k)^2*binomial(2*k, k)/(k+1)) \\ Andrew Howroyd, Dec 13 2024

Crossrefs

Cf. A000108, A003763, A086618, A143246, A209077, A222065, A238116, A238117, A238118.

Sequence in context: A047763 A259621 A026993 * A228959 A302734 A319228

Adjacent sequences: A238112 A238113 A238114 * A238116 A238117 A238118

Keyword

nonn,changed

Author

N. J. A. Sloane, Mar 05 2014

Status

approved