A143246 -id:A143246 - cp's OEIS frontend

A222065 a(n) = A143246(2n).

2, 12, 2144, 9277152, 934520913216, 2152453777211211412, 112252999240982874562527216, 131765033045251672652319572331061144, 3467852755777932367855581588111341658695967892

Offset: 1

N. J. A. Sloane, Feb 08 2013

nonn

Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv preprint arXiv:1402.0545 [math.CO], 2014.
Index entries for sequences related to graphs, Hamiltonian

Cf. A143246.

A096969 Number of ways to number the cells of an n X n square grid with 1,2,3,...,n^2 so that successive integers are in adjacent cells (horizontally or vertically).

Original entry on oeis.org

1, 8, 40, 552, 8648, 458696, 27070560, 6046626568, 1490832682992, 1460089659025264, 1573342970540617696, 6905329711608694708440, 33304011435341069362631160, 663618176813467308855850585056, 14527222735920532980525200234503048

Offset: 1

John W. Layman, Jul 16 2004, at the suggestion of Leroy Quet, Jul 05 2004

Number of directed Hamiltonian paths in (n X n)-grid graph. - Max Alekseyev, May 03 2009

			One of the 8648 numberings of a 5 X 5 grid is
.
  3---2---1  20--21
  |           |   |
  4  17--18--19  22
  |   |           |
  5  16--15--14  23
  |           |   |
  6   9--10  13  24
  |   |   |   |   |
  7---8  11--12  25

Andrew Howroyd, Table of n, a(n) for n = 1..17
Nicolas Bělohoubek, All possible paths in 4th term (552) presented by A..D 1..4 coordination system.
Nicolas Bělohoubek, All possible paths in 5th term (8648) presented by A..E 1..5 coordination system.
Nicolas Bělohoubek, All possible paths in 5th term (8648) in image, blue to red.
Stéphane Duguay and Steven Pigeon, Comparison of Pixel Correlation Induced by Space-Filling Curves on 2D Image Data, The 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (Metz, France, 2019) Vol. 1, 294-297.
Mary Grace Hanson and David A. Nash, Minimal and maximal Numbrix puzzles, arXiv:1706.09389 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
Index entries for sequences related to graphs, Hamiltonian

Cf. A120443, A096970, A143246, A137891, A158651.

Conjecture: Limit_{n->oo} log_(n+1)!(a(n+1)) - log_n!(a(n)) = c, where 0.09 < c < 0.11. - Nicolas Bělohoubek, Jun 12 2022

a(7) from Giovanni Resta, May 12 2006

a(8)-a(15) added by Andrew Howroyd, Dec 20 2015

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

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Mar 05 2014

nonn

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.

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

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

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

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)

A238116 Number of continuations arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

Original entry on oeis.org

1, 14, 162, 1966, 25567, 351880, 5056350, 75100735, 1144833705, 17821104101

Offset: 1

N. J. A. Sloane, Mar 05 2014

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

Cf. A003763, A143246, A209077, A222065, A238115, A238117, A238118.

A238117 Number of states with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

Original entry on oeis.org

1, 4, 14, 40, 120, 320, 946, 2496, 7418, 19616

Offset: 1

N. J. A. Sloane, Mar 05 2014

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

Cf. A003763, A143246, A209077, A222065, A238115, A238116, A238118.

A238118 Number of continuations with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

Original entry on oeis.org

1, 6, 20, 101, 327, 1560, 5333, 24727, 88422, 403552

Offset: 1

N. J. A. Sloane, Mar 05 2014

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

Cf. A003763, A143246, A209077, A222065, A238115, A238116, A238117.

cp's OEIS Frontend

A222065 a(n) = A143246(2n).

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A096969 Number of ways to number the cells of an n X n square grid with 1,2,3,...,n^2 so that successive integers are in adjacent cells (horizontally or vertically).

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

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A238116 Number of continuations arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

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A238117 Number of states with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

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A238118 Number of continuations with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.

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