A267232 T(n,k)=Number of length-n 0..k arrays with no following elements greater than or equal to the first repeated value.

2, 3, 4, 4, 9, 5, 5, 16, 21, 6, 6, 25, 54, 47, 7, 7, 36, 110, 176, 103, 8, 8, 49, 195, 470, 564, 223, 9, 9, 64, 315, 1030, 1980, 1790, 479, 10, 10, 81, 476, 1981, 5375, 8274, 5646, 1023, 11, 11, 100, 684, 3472, 12327, 27854, 34396, 17732, 2175, 12, 12, 121, 945, 5676

Offset

1,1

Comments

Table starts

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

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

..5...21.....54.....110......195.......315.......476........684........945

..6...47....176.....470.....1030......1981......3472.......5676.......8790

..7..103....564....1980.....5375.....12327.....25088......46704......81135

..8..223...1790....8274....27854.....76237....180292.....382404.....745548

..9..479...5646...34396...143695....469623...1291052....3121008....6830757

.10.1023..17732..142474...738990...2884909...9222184...25415028...62455218

.11.2175..55512..588596..3791775..17686215..65755592..206617680..570177387

.12.4607.173354.2426738.19421854.108259885.468196540.1677626052.5199327816

Links

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

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2) for n>3

k=2: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4

k=3: a(n) = 9*a(n-1) -29*a(n-2) +39*a(n-3) -18*a(n-4) for n>5

k=4: a(n) = 14*a(n-1) -75*a(n-2) +190*a(n-3) -224*a(n-4) +96*a(n-5) for n>6

k=5: [order 6] for n>7

k=6: [order 7] for n>8

k=7: [order 8] for n>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 + (3/2)*n

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

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

n=6: a(n) = n^6 + (197/60)*n^5 + 3*n^4 + (3/4)*n^3 - (1/30)*n

n=7: a(n) = n^7 + (69/20)*n^6 + (7/2)*n^5 + (7/6)*n^4 - (7/60)*n^2

Example

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

Crossrefs

Column 1 is A000027(n+2).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A160378(n+1).

Sequence in context: A241037 A097093 A056877 * A269606 A269640 A269409

Adjacent sequences: A267229 A267230 A267231 * A267233 A267234 A267235

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 12 2016

Status

approved