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A302309
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 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, 3, 3, 4, 5, 11, 6, 8, 8, 21, 13, 10, 16, 13, 31, 26, 33, 21, 32, 21, 113, 48, 66, 58, 42, 64, 34, 363, 121, 194, 153, 153, 86, 128, 55, 813, 275, 663, 445, 380, 336, 179, 256, 89, 1751, 600, 2048, 1595, 1271, 1090, 937, 370, 512, 144, 5001, 1296, 5790, 4772, 5715
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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...3...11...21....31....113.....363......813......1751.......5001
...4...6...13...26....48....121.....275......600......1296.......2998
...8..10...33...66...194....663....2048.....5790.....17761......58980
..16..21...58..153...445...1595....4772....15249.....49634.....166329
..32..42..153..380..1271...5715...18992....70289....276303....1198933
..64..86..336.1090..3915..18990...76642...360898...1695748....9408402
.128.179..937.3120.12420..73663..364922..2150420..13123505...95790405
.256.370.2449.9130.42897.312122.1991487.15392485.124691962.1235540899
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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) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 60] for n>61
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 15] for n>16
n=4: [order 61] for n>64
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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..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
..0..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1
..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0. .0..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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