A223374 - OEIS

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A223374

3 X 3 square grid graph coloring a rectangular array: number of n X 3 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

68, 912, 13232, 192752, 2812608, 41044048, 598980512, 8741293936, 127567402912, 1861673117136, 27168612726112, 396489050362864, 5786223905786400, 84442089417201488, 1232318612693585248, 17984018624753407088

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Column 3 of A223379.

LINKS

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

FORMULA

Empirical: a(n) = 221*a(n-2) - 1718*a(n-4) + 1872*a(n-6) for n>7.

Empirical g.f.: 4*x*(17 + 228*x - 449*x^2 - 2200*x^3 + 1290*x^4 + 3168*x^5 - 144*x^6) / (1 - 221*x^2 + 1718*x^4 - 1872*x^6). - Colin Barker, Aug 20 2018

EXAMPLE

Some solutions for n=3:

..1..4..7....6..7..6....5..8..7....7..4..3....3..4..7....8..5..4....8..7..6

..4..7..4....7..6..3....4..7..4....4..3..4....4..7..4....5..4..7....7..6..3

..7..8..5....6..3..6....3..4..7....3..4..5....5..8..5....2..5..8....4..7..6

Vertex neighbors:

0 -> 1 3

1 -> 0 2 4

2 -> 1 5

3 -> 0 4 6

4 -> 3 1 5 7

5 -> 4 2 8

6 -> 3 7

7 -> 6 4 8

8 -> 7 5

CROSSREFS

Cf. A223379.

Sequence in context: A039507 A250144 A250338 * A360656 A254645 A281049

Adjacent sequences: A223371 A223372 A223373 * A223375 A223376 A223377

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 19 2013

STATUS

approved