A223423 T(n,k)=3-level binary fanout graph coloring a rectangular array: number of nXk 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

7, 12, 12, 26, 40, 26, 48, 136, 136, 48, 104, 464, 868, 464, 104, 192, 1584, 4720, 4720, 1584, 192, 416, 5408, 29912, 47872, 29912, 5408, 416, 768, 18464, 163168, 486016, 486016, 163168, 18464, 768, 1664, 63040, 1033328, 4934272, 9210784, 4934272

Offset: 1

Author

R. H. Hardin Mar 20 2013

Keywords

• nonn
• tabl

Comments

Table starts

....7.....12........26..........48............104..............192

...12.....40.......136.........464...........1584.............5408

...26....136.......868........4720..........29912...........163168

...48....464......4720.......47872.........486016..........4934272

..104...1584.....29912......486016........9210784........150006016

..192...5408....163168.....4934272......150006016.......4565849088

..416..18464...1033328....50097024.....2844612736.....139114196992

..768..63040...5638336...508632832....46345527296....4240305623040

.1664.215232..35704800..5164146176...878977950208..129279082045440

.3072.734848.194827648.52431620096.14321836797952.3941937218551808

Examples

			Some solutions for n=3 k=4
..5..2..6..2....5..2..0..1....1..3..1..0....1..0..1..4....0..2..6..2
..2..0..2..6....2..6..2..0....3..1..4..1....4..1..4..1....1..0..2..0
..0..1..0..2....6..2..0..1....1..4..1..0....1..3..1..4....4..1..0..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..544

Crossrefs

Column 2 is A056236(n+1)

Formula

Empirical for column k:

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

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

k=3: a(n) = 38*a(n-2) -120*a(n-4) +32*a(n-6)

k=4: a(n) = 14*a(n-1) -36*a(n-2) -40*a(n-3) +88*a(n-4) +32*a(n-5) -32*a(n-6)

k=5: a(n) = 392*a(n-2) -26768*a(n-4) +353408*a(n-6) -1274624*a(n-8) +1441792*a(n-10) -307200*a(n-12) for n>13

k=6: [order 18]

k=7: [order 36]