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A250387
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T(n,k)=Number of length n+3 0..k arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms
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13
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6, 42, 6, 156, 78, 6, 420, 432, 146, 6, 930, 1560, 1208, 274, 6, 1806, 4350, 5848, 3384, 514, 6, 3192, 10206, 20518, 21950, 9480, 966, 6, 5256, 21168, 58114, 96866, 82398, 26578, 1816, 6, 8190, 40032, 141344, 331128, 457366, 309452, 74528, 3414, 6, 12210
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OFFSET
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1,1
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COMMENTS
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Table starts
.6....42.....156......420........930........1806........3192.........5256
.6....78.....432.....1560.......4350.......10206.......21168........40032
.6...146....1208.....5848......20518.......58114......141344.......306816
.6...274....3384....21950......96866......331128......944272......2352468
.6...514....9480....82398.....457366.....1886948.....6308960.....18038628
.6...966...26578...309452....2160160....10755158....42158796....138336744
.6..1816...74528..1162292...10203222....61304844...281731072...1060924200
.6..3414..208998..4365720...48194820...349446100..1882722300...8136444312
.6..6418..586102.16398414..227649458..1991900312.12581692558..62400176438
.6.12066.1643650.61595866.1075313612.11354195442.84080003928.478561255176
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LINKS
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FORMULA
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Empirical for column k, apparently recurrence of order 7*k-4:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +2*a(n-2) -a(n-3) +3*a(n-4) -a(n-5) -7*a(n-6) +a(n-7) +a(n-10)
k=3: [order 17]
k=4: [order 24]
k=5: [order 31]
k=6: [order 38]
k=7: [order 45]
Empirical for row n, apparently polynomial of degree n+3:
n=1: a(n) = n^4 + 2*n^3 + 2*n^2 + n
n=2: a(n) = n^5 + (3/2)*n^4 + 2*n^3 + (3/2)*n^2
n=3: a(n) = n^6 + (16/15)*n^5 + (13/6)*n^4 + (5/3)*n^3 - (1/6)*n^2 + (4/15)*n
n=4: [polynomial of degree 7]
n=5: [polynomial of degree 8]
n=6: [polynomial of degree 9]
n=7: [polynomial of degree 10]
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EXAMPLE
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Some solutions for n=4 k=4
..3....4....1....4....0....4....2....1....1....1....0....0....1....3....4....0
..2....2....2....2....1....0....3....2....4....3....1....0....1....0....0....3
..3....3....0....4....2....2....4....3....3....2....3....3....0....3....4....0
..1....1....0....2....3....1....0....0....2....4....2....2....0....0....0....2
..3....0....4....3....4....4....4....1....4....1....3....1....1....4....2....1
..0....4....4....2....4....0....1....0....4....4....0....3....2....0....3....4
..4....2....2....3....2....3....0....2....3....0....0....4....2....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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