A222334 T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,1.

2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 7, 9, 2, 3, 4, 7, 11, 13, 2, 3, 4, 7, 11, 17, 19, 2, 3, 4, 7, 11, 18, 27, 28, 2, 3, 4, 7, 11, 18, 29, 42, 41, 2, 3, 4, 7, 11, 18, 29, 46, 66, 60, 2, 3, 4, 7, 11, 18, 29, 47, 74, 104, 88, 2, 3, 4, 7, 11, 18, 29, 47, 76, 118, 163, 129, 2, 3, 4, 7, 11, 18, 29, 47

Offset: 1

Author

R. H. Hardin Feb 15 2013

Keywords

• nonn
• tabl

Comments

Table starts

....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2

....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3

....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4

....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7

....9...11....11....11....11....11....11....11....11....11....11

...13...17....18....18....18....18....18....18....18....18....18

...19...27....29....29....29....29....29....29....29....29....29

...28...42....46....47....47....47....47....47....47....47....47

...41...66....74....76....76....76....76....76....76....76....76

...60..104...118...122...123...123...123...123...123...123...123

...88..163...189...197...199...199...199...199...199...199...199

..129..256...303...317...321...322...322...322...322...322...322

..189..402...485...511...519...521...521...521...521...521...521

..277..631...777...824...838...842...843...843...843...843...843

..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364

..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207

..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571

.1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778

.1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349

.2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127

Empirical: for n<=2k+1, T(n,k)=A080023(n)=A169985(n), which is A000032(n) for n>=2. - Danny Rorabaugh, Mar 13 2015

Examples

			Some solutions for n=6 k=4, one extended zero followed by filtered positions
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....1....0....1....0....1....0....0....1....0....1....0....0
..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1
..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0
..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0
..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0
..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9501

Crossrefs

Column 1 is A000930(n+2).

Column 2 is A222122.

Columns 3 to 7 are A222329 to A222333.

Cf. A000032, A080023, A169985.

Formula

Empirical for column k:

k=1: a(n) = a(n-1)+a(n-3)

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

k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)

k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)

k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)

k=6: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)

k=7: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)+a(n-15)