A299682 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 45, 45, 73, 32, 64, 157, 147, 211, 147, 157, 64, 128, 353, 506, 1477, 1477, 506, 353, 128, 256, 869, 1561, 7279, 13369, 7279, 1561, 869, 256, 512, 1993, 5017, 35408, 95471, 95471, 35408, 5017, 1993, 512

Offset

1,2

Comments

Table starts

...1....2.....4.......8.......16.........32...........64............128

...2....7....13......29.......73........157..........353............869

...4...13....20......45......147........506.........1561...........5017

...8...29....45.....211.....1477.......7279........35408.........196107

..16...73...147....1477....13369......95471.......757628........6503333

..32..157...506....7279....95471....1247427.....16311888......226655504

..64..353..1561...35408...757628...16311888....346275749.....7835688567

.128..869..5017..196107..6503333..226655504...7835688567...289785610230

.256.1993.16429.1040287.52948378.3113437608.174961291252.10547510714203

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6

k=3: [order 16] for n>17

k=4: [order 61] for n>64

Example

Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0. .0..1..0..0
..0..0..0..1. .1..1..0..1. .0..0..0..1. .1..0..1..0. .1..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..1. .1..0..0..0
..1..0..1..1. .1..0..1..1. .0..1..0..1. .1..0..0..1. .1..0..0..1
..1..0..1..0. .0..1..0..0. .1..1..0..0. .0..0..0..0. .1..0..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A299879 A299015 A299806 * A300314 A280604 A301323

Adjacent sequences: A299679 A299680 A299681 * A299683 A299684 A299685

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2018

Status

approved