A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 171, 108, 16, 32, 401, 1008, 1008, 401, 32, 64, 1490, 5930, 9541, 5930, 1490, 64, 128, 5536, 34976, 91370, 91370, 34976, 5536, 128, 256, 20569, 206266, 877044, 1423344, 877044, 206266, 20569, 256, 512, 76424, 1216562

Offset

1,2

Comments

Table starts

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

...2.....8......29.......108.........401..........1490.............5536

...4....29.....171......1008........5930.........34976...........206266

...8...108....1008......9541.......91370........877044..........8414314

..16...401....5930.....91370.....1423344......22207589........346263718

..32..1490...34976....877044....22207589.....564002959......14319674594

..64..5536..206266...8414314...346263718...14319674594.....592006690060

.128.20569.1216562..80726964..5399605493..363595763125...24472344492129

.256.76424.7175157.774477323.84198470831.9231743942243.1011614229196954

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 40]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A300472 A326105 A300811 * A302265 A302965 A302808

Adjacent sequences: A301447 A301448 A301449 * A301451 A301452 A301453

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 21 2018

Status

approved