A267471 T(n,k)=Number of length-n 0..k arrays with no following elements larger than the first repeated value.

2, 3, 4, 4, 9, 7, 5, 16, 24, 12, 6, 25, 58, 62, 21, 7, 36, 115, 204, 160, 38, 8, 49, 201, 515, 712, 418, 71, 9, 64, 322, 1096, 2285, 2490, 1112, 136, 10, 81, 484, 2072, 5921, 10119, 8770, 3018, 265, 11, 100, 693, 3592, 13216, 31880, 44901, 31200, 8352, 522, 12, 121

Offset: 1

Author

R. H. Hardin, Jan 15 2016

Keywords

• nonn
• tabl

Comments

Table starts

...2.....3......4.......5........6.........7.........8..........9.........10

...4.....9.....16......25.......36........49........64.........81........100

...7....24.....58.....115......201.......322.......484........693........955

..12....62....204.....515.....1096......2072......3592.......5829.......8980

..21...160....712....2285.....5921.....13216.....26440......48657......83845

..38...418...2490...10119....31880.....83972....193852.....404589.....779938

..71..1112...8770...44901...171601....532840...1418740....3357537....7240267

.136..3018..31200..200119...925176...3381860..10378144...27838701...67140808

.265..8352.112300..897301..5002641..21491464..75944464..230790033..622347697

.522.23522.409254.4052183.27155800.136856180.556295860.1914051597.5768860606

Examples

			Some solutions for n=6 k=4
..0....1....1....4....0....1....0....4....1....2....3....4....4....1....0....3
..4....0....4....0....4....0....3....0....2....3....1....4....3....4....1....0
..4....2....2....4....3....4....2....4....0....0....2....4....2....0....3....2
..0....3....4....0....3....4....3....3....1....1....4....2....4....4....4....3
..2....4....1....1....0....0....1....1....2....1....3....1....3....2....1....3
..4....4....1....1....3....2....0....2....0....0....0....1....4....3....1....1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A005126(n-1).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A081436.

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)

k=2: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4)

k=3: a(n) = 13*a(n-1) -65*a(n-2) +155*a(n-3) -174*a(n-4) +72*a(n-5)

k=4: a(n) = 19*a(n-1) -145*a(n-2) +565*a(n-3) -1174*a(n-4) +1216*a(n-5) -480*a(n-6)

k=5: [order 7]

k=6: [order 8]

k=7: [order 9]

Empirical for row n:

n=1: a(n) = n + 1

n=2: a(n) = n^2 + 2*n + 1

n=3: a(n) = n^3 + (5/2)*n^2 + (5/2)*n + 1

n=4: a(n) = n^4 + (17/6)*n^3 + 4*n^2 + (19/6)*n + 1

n=5: a(n) = n^5 + (37/12)*n^4 + (11/2)*n^3 + (77/12)*n^2 + 4*n + 1

n=6: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1

n=7: a(n) = n^7 + (69/20)*n^6 + (17/2)*n^5 + (97/6)*n^4 + 20*n^3 + (893/60)*n^2 + 6*n + 1