A299089 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 92, 88, 16, 32, 298, 354, 354, 298, 32, 64, 1012, 1387, 1617, 1387, 1012, 64, 128, 3440, 5470, 7722, 7722, 5470, 3440, 128, 256, 11700, 21484, 36667, 46456, 36667, 21484, 11700, 256, 512, 39804, 84425, 173524, 273360, 273360

Offset

1,2

Comments

Table starts

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

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

...4....26.....92.....354.....1387......5470.......21484........84425

...8....88....354....1617.....7722.....36667......173524.......822065

..16...298...1387....7722....46456....273360.....1598956......9400094

..32..1012...5470...36667...273360...2001653....14514670....105596164

..64..3440..21484..173524..1598956..14514670...129999453...1166134994

.128.11700..84425..822065..9400094.105596164..1166134994..12899638332

.256.39804.331838.3897261.55296169.769538056.10493701031.143316205219

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 17] for n>19

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A301841 A302069 A298195 * A299345 A299852 A299008

Adjacent sequences: A299086 A299087 A299088 * A299090 A299091 A299092

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 02 2018

Status

approved