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A232316
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
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14
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2, 5, 5, 16, 24, 13, 52, 139, 115, 34, 169, 853, 1202, 551, 89, 549, 5241, 14042, 10409, 2640, 233, 1784, 32089, 164014, 231454, 90157, 12649, 610, 5797, 196698, 1905436, 5142441, 3815483, 780922, 60605, 1597, 18837, 1205422, 22161823, 113293694
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OFFSET
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1,1
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COMMENTS
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Table starts
.....2.......5.........16............52..............169.................549
.....5......24........139...........853.............5241...............32089
....13.....115.......1202.........14042...........164014.............1905436
....34.....551......10409........231454..........5142441...........113293694
....89....2640......90157.......3815483........161243887..........6736602042
...233...12649.....780922......62897985.......5055954492........400571676322
...610...60605....6764246....1036869496.....158534446141......23818815015639
..1597..290376...58591124...17092731689....4971005036586....1416315842358249
..4181.1391275..507509767..281772661177..155870804492221...84217060496525106
.10946.6665999.4395993154.4645005493684.4887484036570530.5007720081104988709
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) -a(n-2)
k=2: a(n) = 5*a(n-1) -a(n-2)
k=3: a(n) = 10*a(n-1) -11*a(n-2) -5*a(n-3) -a(n-4)
k=4: a(n) = 19*a(n-1) -44*a(n-2) +43*a(n-3) -19*a(n-4) +4*a(n-5) -2*a(n-6) for n>7
k=5: [order 12] for n>13
k=6: [order 18] for n>20
k=7: [order 37] for n>40
Empirical for row n:
n=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>5
n=2: [order 12] for n>14
n=3: [order 32] for n>34
n=4: [order 78] for n>82
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EXAMPLE
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Some.solutions.for.n=3.k=4
..0..0..0..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..0
..0..0..1..1..1....0..1..1..0..0....0..0..0..1..1....0..1..1..0..1
..1..1..0..0..0....1..0..0..1..1....0..0..1..1..1....0..0..0..1..0
..1..1..1..1..1....1..1..1..0..0....0..0..0..0..0....1..1..1..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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