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A189326
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T(n,k)=Number of nondecreasing arrangements of n+2 numbers in 0..k with the last equal to k and each after the second equal to the sum of one or two of the preceding four
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15
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2, 4, 2, 5, 6, 2, 7, 7, 8, 2, 8, 12, 11, 10, 2, 10, 12, 20, 16, 12, 2, 11, 18, 21, 32, 22, 14, 2, 13, 17, 36, 33, 49, 28, 16, 2, 14, 24, 31, 64, 54, 70, 34, 18, 2, 16, 22, 49, 51, 110, 84, 94, 40, 20, 2, 17, 30, 42, 95, 91, 179, 119, 120, 46, 22, 2, 19, 27, 63, 76, 179, 157, 275, 157
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OFFSET
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1,1
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COMMENTS
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Table starts
.2..4..5...7...8..10..11...13...14...16...17...19...20...22...23....25...26
.2..6..7..12..12..18..17...24...22...30...27...36...32...42...37....48...42
.2..8.11..20..21..36..31...49...42...63...51...79...60...93...72...105...80
.2.10.16..32..33..64..51...95...76..122...91..166..102..185..141...214..137
.2.12.22..49..54.110..91..179..154..238..190..360..215..376..333...453..290
.2.14.28..70..84.179.157..321..283..461..390..720..482..784..747...988..684
.2.16.34..94.119.275.253..548..477..845..725.1375..951.1608.1522..2126.1511
.2.18.40.120.157.393.374..866..775.1426.1261.2448.1761.3006.2890..4232.3063
.2.20.46.148.195.528.509.1267.1161.2230.2033.4069.3000.5252.5080..7749.5692
.2.22.52.178.233.676.649.1733.1606.3234.3005.6291.4691.8502.8350.13138.9724
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LINKS
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FORMULA
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Empirical: T(n,1) = 2
Empirical: T(n,2) = 2*n + 2
Empirical: T(n,3) = 6*n - 8 for n>3
Empirical: T(n,4) = n^2 + 11*n - 32 for n>5
Empirical: T(n,5) = 38*n - 147 for n>6
Empirical: T(n,6) = 6*n^2 + 34*n - 264 for n>8
Empirical: T(n,7) = 140*n - 751 for n>8
Empirical: T(n,8) = (1/3)*n^3 + 10*n^2 + (587/3)*n - 1558 for n>10
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EXAMPLE
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Some solutions for n=5 k=3
..1....0....1....0....1....1....0....1....0....0....3....0....1....1....1....1
..2....1....1....1....2....1....1....3....1....1....3....1....1....1....1....2
..2....1....1....1....2....1....1....3....1....1....3....1....2....2....1....3
..3....1....1....1....2....1....2....3....2....2....3....1....2....2....2....3
..3....2....1....1....3....2....2....3....2....3....3....2....3....2....3....3
..3....2....2....2....3....3....2....3....3....3....3....3....3....3....3....3
..3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
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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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