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A223449
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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
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9
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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