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

Author

R. H. Hardin May 04 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 is A001651(n+1)

Row 2 is A189327

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