A300267 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 95, 88, 16, 32, 298, 375, 375, 298, 32, 64, 1012, 1526, 2030, 1526, 1012, 64, 128, 3440, 6198, 12324, 12324, 6198, 3440, 128, 256, 11700, 25034, 71529, 138215, 71529, 25034, 11700, 256, 512, 39804, 101312, 412094

Offset

1,2

Comments

Table starts

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

...2.....8.....26.......88........298........1012..........3440...........11700

...4....26.....95......375.......1526........6198.........25034..........101312

...8....88....375.....2030......12324.......71529........412094.........2398145

..16...298...1526....12324.....138215.....1333242......12622937.......125646087

..32..1012...6198....71529....1333242....20341795.....298472434......4660242199

..64..3440..25034...412094...12622937...298472434....6717267728....162737578821

.128.11700.101312..2398145..125646087..4660242199..162737578821...6293324571337

.256.39804.410252.13965762.1244747820.72718129316.3942079842968.243019177909127

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) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)

k=3: [order 18] for n>19

k=4: [order 64] for n>66

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A299008 A299675 A299753 * A318016 A320402 A208709

Adjacent sequences: A300264 A300265 A300266 * A300268 A300269 A300270

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2018

Status

approved