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A242584
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T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (with a!=b) and new values 0..k introduced in 0..k order
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8
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7, 13, 12, 14, 35, 21, 14, 45, 97, 37, 14, 46, 159, 271, 65, 14, 46, 174, 587, 757, 114, 14, 46, 175, 723, 2209, 2115, 200, 14, 46, 175, 744, 3192, 8391, 5913, 351, 14, 46, 175, 745, 3453, 14648, 32020, 16535, 616, 14, 46, 175, 745, 3481, 17178, 68819, 122439, 46237
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OFFSET
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1,1
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COMMENTS
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Table starts
....7.....13......14......14.......14.......14.......14.......14.......14
...12.....35......45......46.......46.......46.......46.......46.......46
...21.....97.....159.....174......175......175......175......175......175
...37....271.....587.....723......744......745......745......745......745
...65....757....2209....3192.....3453.....3481.....3482.....3482.....3482
..114...2115....8391...14648....17178....17634....17670....17671....17671
..200...5913...32020...68819....90033....95729....96472....96517....96518
..351..16535..122439..327821...489821...550503...562109...563256...563311
..616..46237..468605.1574161..2734513..3316400..3469255..3491141..3492837
.1081.129291.1794215.7594177.15534111.20716789.22511261.22860029.22898822
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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) -a(n-2) +a(n-3)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +6*a(n-3) -4*a(n-4)
k=3: a(n) = 7*a(n-1) -18*a(n-2) +32*a(n-3) -45*a(n-4) +37*a(n-5) -21*a(n-6) +9*a(n-7)
k=4: [order 10]
k=5: [order 13]
k=6: [order 16]
k=7: [order 19]
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EXAMPLE
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Some solutions for n=4 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....1
..0....2....0....2....2....2....2....2....2....2....2....1....1....2....2....2
..2....1....2....2....3....0....0....3....3....1....3....2....1....1....0....2
..1....2....0....0....4....3....3....0....3....0....4....3....2....3....2....3
..3....3....0....3....1....3....2....4....3....3....3....2....1....3....3....4
..2....2....3....4....2....4....4....3....2....1....3....1....2....0....4....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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