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A269097
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T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
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8
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0, 4, 4, 24, 96, 24, 108, 1152, 1152, 108, 432, 11424, 31296, 11424, 432, 1620, 103488, 715320, 715320, 103488, 1620, 5832, 889056, 15024096, 37963968, 15024096, 889056, 5832, 20412, 7375872, 300056400, 1856325000, 1856325000, 300056400, 7375872
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OFFSET
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1,2
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COMMENTS
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Table starts
......0..........4.............24................108....................432
......4.........96...........1152..............11424.................103488
.....24.......1152..........31296.............715320...............15024096
....108......11424.........715320...........37963968.............1856325000
....432.....103488.......15024096.........1856325000...........211625837280
...1620.....889056......300056400........86415197088.........22984646281176
...5832....7375872.....5795398368......3892946216856.......2416707037884480
..20412...59698464...109294975080....171307237216320.....248267055360211392
..69984..474360768..2024660774592...7406621052177000...25062609875880382656
.236196.3715826016.36988673403168.315868041326151072.2495854741014485439624
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..264
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FORMULA
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Empirical for column k:
k=1: a(n) = 6*a(n-1) -9*a(n-2)
k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5
k=4: [order 6] for n>7
k=5: [order 14] for n>15
k=6: [order 26] for n>27
k=7: [order 64] for n>65
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..3..2. .0..0..2..2. .2..2..2..3. .0..2..2..0. .0..0..1..1
..0..3..1..0. .0..2..3..3. .0..2..2..2. .0..2..0..0. .0..2..0..0
..0..2..3..2. .1..1..1..3. .2..0..0..3. .0..2..3..2. .2..2..1..1
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CROSSREFS
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Column 1 is A120908.
Sequence in context: A058166 A092897 A269152 * A307552 A171633 A221276
Adjacent sequences: A269094 A269095 A269096 * A269098 A269099 A269100
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 19 2016
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STATUS
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approved
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