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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A005126(n-1).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A081436.

Sequence in context: A269678 A269467 A228461 * A268457 A244940 A244832

Adjacent sequences: A267468 A267469 A267470 * A267472 A267473 A267474

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2016

Status

approved