A223449 T(n,k)=4-level binary fanout graph coloring a rectangular array: number of nXk 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 1,3 3,5 3,6 1,4 4,7 4,8 0,2 2,9 9,11 9,12 2,10 10,13 10,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

15, 28, 28, 66, 104, 66, 144, 408, 408, 144, 336, 1616, 2988, 1616, 336, 752, 6432, 20640, 20640, 6432, 752, 1752, 25664, 149120, 262368, 149120, 25664, 1752, 3936, 102528, 1050624, 3364544, 3364544, 1050624, 102528, 3936, 9168, 409856, 7557696

Offset

1,1

Comments

Table starts

....15......28.........66...........144.............336................752

....28.....104........408..........1616............6432..............25664

....66.....408.......2988.........20640..........149120............1050624

...144....1616......20640........262368.........3364544...........43139520

...336....6432.....149120.......3364544........78731136.........1806815040

...752...25664....1050624......43139520......1806815040........75601620736

..1752..102528....7557696.....553773760.....42196917280......3173584196608

..3936..409856...53547904....7110140800....972415126144....133184053106688

..9168.1638912..384685440...91312361088..22683600827456...5592572908886016

.20608.6554624.2730236928.1172796624128.523428338294528.234829512186605568

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-2) -4*a(n-4)

k=2: a(n) = 6*a(n-1) -8*a(n-2) for n>3

k=3: a(n) = 70*a(n-2) -1024*a(n-4) +2832*a(n-6) -1792*a(n-8) +128*a(n-10)

k=4: [order 11] for n>12

k=5: [order 32]

k=6: [order 44] for n>45

Example

Some solutions for n=3 k=4
..2..9.12..9....2..9.11..9....7..4..1..0....0..1..3..5....9..2..0..2
..9..2..9.11....9.12..9.12....4..8..4..1....1..3..6..3....2.10..2.10
.12..9.12..9...11..9.12..9....7..4..8..4....0..1..3..1...10..2.10.13

Crossrefs

Sequence in context: A230649 A229195 A073766 * A031334 A178958 A099808

Adjacent sequences: A223446 A223447 A223448 * A223450 A223451 A223452

Keyword

nonn,tabl

Author

R. H. Hardin Mar 20 2013

Status

approved