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

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

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 * A373286 A260985 A322448

Adjacent sequences: A223399 A223400 A223401 * A223403 A223404 A223405

Keyword

nonn,tabl

Author

R. H. Hardin Mar 19 2013

Status

approved