A190041 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 three

2, 4, 2, 5, 6, 2, 7, 7, 8, 2, 8, 12, 10, 10, 2, 10, 12, 18, 14, 12, 2, 11, 18, 16, 27, 18, 14, 2, 13, 17, 30, 23, 39, 22, 16, 2, 14, 24, 22, 47, 33, 53, 26, 18, 2, 16, 22, 40, 31, 72, 45, 69, 30, 20, 2, 17, 30, 31, 65, 43, 107, 57, 87, 34, 22, 2, 19, 27, 49, 49, 105, 60, 151, 69, 107

Offset

1,1

Comments

Table starts

.2..4..5...7..8..10..11..13..14..16..17...19..20...22...23...25..26...28..29

.2..6..7..12.12..18..17..24..22..30..27...36..32...42...37...48..42...54..47

.2..8.10..18.16..30..22..40..31..49..36...64..41...71...53...81..55...97..61

.2.10.14..27.23..47..31..65..49..76..52..113..58..109...92..132..78..167..87

.2.12.18..39.33..72..43.105..69.123..72..190..83..169..151..217.108..276.120

.2.14.22..53.45.107..60.164.100.189..99..311.121..251..241..358.146..447.167

.2.16.26..69.57.151..80.246.144.284.138..492.178..372..364..583.195..717.239

.2.18.30..87.69.203.100.349.200.409.189..754.258..545..540..927.267.1109.341

.2.20.34.107.81.263.120.472.264.560.245.1108.352..775..778.1424.364.1677.484

.2.22.38.129.93.331.140.617.336.735.301.1561.448.1053.1072.2094.474.2449.657

Links

R. H. Hardin, Table of n, a(n) for n = 1..4434

Formula

Empirical: T(n,1) = 2

Empirical: T(n,2) = 2*n + 2

Empirical: T(n,3) = 4*n - 2 for n>2

Empirical: T(n,4) = n^2 + 3*n - 1 for n>3

Empirical: T(n,5) = 12*n - 27 for n>4

Empirical: T(n,6) = 4*n^2 - 8*n + 11 for n>5

Empirical: T(n,7) = 20*n - 60 for n>5

Empirical: T(n,8) = (1/3)*n^3 + 2*n^2 + (50/3)*n - 83 for n>6

Example

Some solutions for n=5 k=3
..2....3....1....1....0....1....0....0....0....0....1....1....1....1....1....1
..3....3....1....1....1....2....1....1....1....3....1....3....1....1....1....2
..3....3....2....1....1....3....1....1....1....3....1....3....1....1....2....2
..3....3....3....1....1....3....2....1....2....3....1....3....1....2....2....3
..3....3....3....2....1....3....3....2....2....3....1....3....2....3....3....3
..3....3....3....3....2....3....3....3....3....3....2....3....2....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)

Row 2 is A189327

Sequence in context: A347098 A229920 A201562 * A189326 A106688 A167977

Adjacent sequences: A190038 A190039 A190040 * A190042 A190043 A190044

Keyword

nonn,tabl

Author

R. H. Hardin May 04 2011

Status

approved