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

1,1

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

Links

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

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)

Example

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

Crossrefs

Column 1 is A000930(n+2).

Column 2 is A222122.

Columns 3 to 7 are A222329 to A222333.

Cf. A000032, A080023, A169985.

Sequence in context: A222027 A222127 A221999 * A340716 A181948 A238943

Adjacent sequences: A222331 A222332 A222333 * A222335 A222336 A222337

Keyword

nonn,tabl

Author

R. H. Hardin Feb 15 2013

Status

approved