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A223402 T(n,k)=4X4 square grid graph coloring a rectangular array: number of nXk 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 9
16, 48, 48, 152, 328, 152, 488, 2360, 2360, 488, 1576, 17280, 39480, 17280, 1576, 5096, 127464, 672784, 672784, 127464, 5096, 16488, 943016, 11561512, 26836512, 11561512, 943016, 16488, 53352, 6985008, 199425400, 1080643264, 1080643264 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.....16.........48............152................488..................1576

.....48........328...........2360..............17280................127464

....152.......2360..........39480.............672784..............11561512

....488......17280.........672784...........26836512............1080643264

...1576.....127464.......11561512.........1080643264..........102163935000

...5096.....943016......199425400........43699580872.........9705525235832

..16488....6985008.....3445747472......1770698081072.......924127826390176

..53352...51763176....59582558136.....71817607508112.....88090590750261080

.172648..383669400..1030635314552...2914205675816528...8401742793556003144

.558696.2843977792.17830297764560.118279017948229984.801551619655700687184

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

k=1: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3)

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

k=3: [order 12] for n>13

k=4: [order 28] for n>29

k=5: [order 94] for n>95

EXAMPLE

Some solutions for n=3 k=4

..4..8..9..5....5..6..2..1....0..1..5..4....8..4..5..6....1..0..1..5

..8..4..5..4....4..5..1..0....4..5..6..5....4..5..1..5....0..1..5..6

.12..8..9..8....0..4..5..1....8..9..5..9....8..9..5..6....1..5..4..5

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

Sequence in context: A235765 A235548 A223440 * A260985 A322448 A264164

Adjacent sequences:  A223399 A223400 A223401 * A223403 A223404 A223405

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 19 2013

STATUS

approved

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Last modified January 26 05:13 EST 2022. Contains 350572 sequences. (Running on oeis4.)