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A318545
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 6, 5, 8, 13, 8, 13, 13, 8, 13, 21, 15, 26, 31, 26, 15, 21, 34, 26, 52, 78, 78, 52, 26, 34, 55, 45, 107, 207, 247, 207, 107, 45, 55, 89, 80, 218, 516, 784, 784, 516, 218, 80, 89, 144, 140, 442, 1288, 2349, 2905, 2349, 1288, 442, 140, 144, 233
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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........144
..2..1...3....5.....8.....15.....26......45.......80.......140........245
..3..3...6...13....26.....52....107.....218......442.......899.......1829
..5..5..13...31....78....207....516....1288.....3270......8271......20866
..8..8..26...78...247....784...2349....7191....22268.....68384.....210050
.13.15..52..207...784...2905..10496...38721...144148....531780....1960675
.21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716
.34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113
.55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5) for n>6
k=3: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8
k=4: [order 13] for n>14
k=5: [order 23] for n>24
k=6: [order 37] for n>38
k=7: [order 63] for n>64
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1. .1..0..0..1
..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
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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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