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A302322
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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13
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1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 65, 81, 16, 32, 136, 177, 281, 264, 32, 64, 360, 519, 953, 1144, 857, 64, 128, 960, 1528, 3559, 4525, 4321, 2785, 128, 256, 2576, 4509, 14022, 20686, 19734, 18093, 9050, 256, 512, 6944, 13329, 55727, 104932, 110035
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2......4.......8.......16........32.........64.........128
...2.....8.....20......52......136.......360........960........2576
...4....25.....65.....177......519......1528.......4509.......13329
...8....81....281.....953.....3559.....14022......55727......218945
..16...264...1144....4525....20686....104932.....529381.....2593409
..32...857...4321...19734...110035....708572....4521584....27478634
..64..2785..18093...96956...659949...5542827...45861206...349722102
.128..9050..72746..458537..3834162..41843808..444688101..4252740185
.256.29407.285199.2098489.21619209.305929316.4176914829.49936266116
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 48] for n>49
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4
n=3: [order 14] for n>15
n=4: [order 57] for n>58
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..1..0. .0..0..1..1. .0..1..0..0
..1..0..0..1. .0..1..1..0. .0..0..1..0. .1..0..0..1. .1..0..1..1
..0..1..0..1. .0..0..0..0. .1..1..1..0. .1..0..1..0. .1..0..1..0
..1..1..0..1. .1..0..0..1. .0..0..1..0. .0..1..1..0. .0..1..1..0
..0..0..1..0. .1..0..0..1. .1..0..1..1. .0..1..1..0. .1..0..0..1
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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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