A299528 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 6 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, 12, 12, 48, 1, 0, 88, 35, 166, 35, 88, 0, 1, 240, 60, 537, 537, 60, 240, 1, 0, 704, 269, 2573, 7116, 2573, 269, 704, 0, 1, 1600, 873, 16538, 26670, 26670, 16538, 873, 1600, 1, 0, 4032, 1985, 83533, 258389, 278292

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.....12.......35........60.........269...........873

.1...16...12....166......537......2573.......16538.........83533

.0...48...35....537.....7116.....26670......258389.......3071901

.1...88...60...2573....26670....278292.....4719927......71687832

.0..240..269..16538...258389...4719927...135080376....3421183432

.1..704..873..83533..3071901..71687832..3421183432..167282094170

.0.1600.1985.420801.19928263.922790506.75654324618.5847633932248

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 17] for n>18

k=4: [order 53] for n>56

Example

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

Crossrefs

Column 2 is A298448.

Sequence in context: A298454 A298834 A299588 * A300146 A100045 A143844

Adjacent sequences: A299525 A299526 A299527 * A299529 A299530 A299531

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 11 2018

Status

approved