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A301884
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
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13
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1, 2, 2, 3, 5, 4, 5, 10, 13, 8, 8, 18, 29, 34, 16, 13, 35, 58, 95, 89, 32, 21, 74, 125, 203, 289, 233, 64, 34, 154, 331, 510, 673, 917, 610, 128, 55, 317, 823, 1754, 1961, 2340, 2841, 1597, 256, 89, 658, 2086, 5463, 8829, 7869, 7883, 8921, 4181, 512, 144, 1370, 5269
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....3.....5......8......13.......21........34.........55..........89
...2....5....10....18.....35......74......154.......317........658........1370
...4...13....29....58....125.....331......823......2086.......5269.......13305
...8...34....95...203....510....1754.....5463.....16452......49611......153498
..16...89...289...673...1961....8829....33853....122356.....439781.....1684392
..32..233...917..2340...7869...46079...223869....981222....4188971....19744757
..64..610..2841..7883..31173..240222..1454613...7734317...39492565...231010966
.128.1597..8921.27175.124795.1258853..9620565..62334085..380963915..2762447554
.256.4181.27801.92411.497909.6603593.63336647.498835686.3652793090.32938593566
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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)
k=3: a(n) = a(n-1) +6*a(n-2) +2*a(n-3)
k=4: a(n) = a(n-1) +12*a(n-2) -2*a(n-3) -38*a(n-4) +a(n-5) +12*a(n-6) -a(n-8)
k=5: [order 7] for n>9
k=6: [order 32] for n>33
k=7: [order 52] for n>54
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7)
n=3: [order 24] for n>25
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..1..1..1. .0..0..1..0. .0..0..1..0
..1..0..0..1. .0..1..0..1. .0..1..0..0. .1..0..0..1. .1..0..1..0
..0..1..0..1. .0..1..0..1. .0..1..1..1. .1..0..1..0. .1..0..1..1
..0..1..0..1. .0..0..0..1. .0..1..0..1. .1..0..1..0. .1..0..0..1
..0..1..0..0. .1..1..0..1. .0..1..1..1. .1..1..1..0. .1..1..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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