A223396 4 X 4 square grid graph coloring a rectangular array: number of n X 2 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

48, 328, 2360, 17280, 127464, 943016, 6985008, 51763176, 383669400, 2843977792, 21081830152, 156277203016, 1158470626096, 8587668090888, 63659878472312, 471907077858304, 3498220894515624, 25932117973637736, 192233359691316016

Offset

1,1

Comments

Column 2 of A223402.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 10*a(n-1) - 18*a(n-2) - 9*a(n-3) + 2*a(n-4).

Empirical g.f.: 8*x*(2 + x)*(3 - 11*x + 2*x^2) / (1 - 10*x + 18*x^2 + 9*x^3 - 2*x^4). - Colin Barker, Aug 20 2018

Example

Some solutions for n=3:
..6.10...10.14...13.14....9.13....8..9....6..2....9..5....9.13....3..7....5..1
.10..6...14.10....9.10...13..9....4..8....7..3...13..9...10.14....2..6....4..5
.14.10...10.14...10.11....9.10....8..9...11..7....9..5...14.15....6..2....0..4
Vertex neighbors:
0 -> 1 4
1 -> 0 2 5
2 -> 1 3 6
3 -> 2 7
4 -> 0 5 8
5 -> 4 1 6 9
6 -> 5 2 7 10
7 -> 6 3 11
8 -> 4 9 12
9 -> 8 5 10 13
10 -> 9 6 11 14
11 -> 10 7 15
12 -> 8 13
13 -> 12 9 14
14 -> 13 10 15
15 -> 14 11

Crossrefs

Cf. A223402.

Sequence in context: A192215 A347613 A280022 * A211735 A211746 A211755

Adjacent sequences: A223393 A223394 A223395 * A223397 A223398 A223399

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved