A189326 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Row 1 is A001651(n+1)

Sequence in context: A229920 A201562 A190041 * A106688 A167977 A267005

Adjacent sequences: A189323 A189324 A189325 * A189327 A189328 A189329

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 20 2011

STATUS

approved