A189326 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.

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

Offset: 1

Author

R. H. Hardin Apr 20 2011

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..3692

Crossrefs

Row 1 is A001651(n+1)

Formula

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