A300146 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 1, 16, 0, 1, 48, 18, 18, 48, 1, 0, 88, 41, 246, 41, 88, 0, 1, 240, 130, 1043, 1043, 130, 240, 1, 0, 704, 510, 5368, 13182, 5368, 510, 704, 0, 1, 1600, 1740, 37739, 78147, 78147, 37739, 1740, 1600, 1, 0, 4032, 5554, 219689, 913701

Offset

1,5

Comments

Table starts

.0....1....0.......1........0..........1............0..............1

.1....4....4......16.......48.........88..........240............704

.0....4....1......18.......41........130..........510...........1740

.1...16...18.....246.....1043.......5368........37739.........219689

.0...48...41....1043....13182......78147.......913701.......11122233

.1...88..130....5368....78147....1048462.....21602016......399714825

.0..240..510...37739...913701...21602016....783899343....25183985328

.1..704.1740..219689.11122233..399714825..25183985328..1507189100633

.0.1600.5554.1245482.99027295.6588098950.731705422933.74614900420199

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 15] for n>17

k=4: [order 40] for n>42

Example

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

Crossrefs

Column 2 is A298448.

Sequence in context: A298834 A299588 A299528 * A100045 A143844 A186759

Adjacent sequences: A300143 A300144 A300145 * A300147 A300148 A300149

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 26 2018

Status

approved