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A233239
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T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order
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13
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1, 2, 3, 6, 19, 11, 23, 271, 313, 48, 99, 4504, 18744, 6046, 236, 452, 79201, 1212549, 1409129, 123352, 1248, 2136, 1419889, 79794804, 338046654, 107709266, 2565169, 6896, 10313, 25622596, 5267525102, 81477098771, 94601758339, 8259321811
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OFFSET
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1,2
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COMMENTS
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Table starts
.......1............2..................6.......................23
.......3...........19................271.....................4504
......11..........313..............18744..................1212549
......48.........6046............1409129................338046654
.....236.......123352..........107709266..............94601758339
....1248......2565169.........8259321811...........26484848685044
....6896.....53692063.......633724470764.........7415057313896849
...39168...1126297996.....48630297616989......2076029517168733114
..226496..23643610702...3731839458899046....581236325493128357679
.1325568.496455294319.286378755661153351.162731637919752077883024
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)
k=3: a(n) = 93*a(n-1) -1273*a(n-2) +1943*a(n-3) -882*a(n-4) +120*a(n-5)
k=4: a(n) = 311*a(n-1) -8722*a(n-2) +10022*a(n-3) -1645*a(n-4) +35*a(n-5)
Empirical for row n:
n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
n=2: a(n) = 23*a(n-1) -81*a(n-2) -143*a(n-3) +82*a(n-4) +120*a(n-5) for n>6
n=3: [order 9] for n>10
n=4: [order 21] for n>22
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..0..2....0..0..1..2....0..1..0..2....0..0..1..0....0..0..1..2
..3..3..0..0....4..0..0..3....1..0..0..0....2..0..2..1....2..0..1..5
..0..3..3..4....3..0..4..2....2..2..0..2....2..1..2..2....1..5..3..5
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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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