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

Author

R. H. Hardin, Jan 12 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

..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

Examples

			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
		

Links

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

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).

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