A299345 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 93, 88, 16, 32, 298, 357, 357, 298, 32, 64, 1012, 1399, 1618, 1399, 1012, 64, 128, 3440, 5513, 7667, 7667, 5513, 3440, 128, 256, 11700, 21642, 36182, 45287, 36182, 21642, 11700, 256, 512, 39804, 85000, 170056, 262230, 262230

Offset

1,2

Comments

Table starts

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

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

...4....26.....93.....357.....1399......5513......21642........85000

...8....88....357....1618.....7667.....36182.....170056.......800122

..16...298...1399....7667....45287....262230....1511085......8755520

..32..1012...5513...36182...262230...1870946...13239850.....94146701

..64..3440..21642..170056..1511085..13239850..114730926....998177623

.128.11700..85000..800122..8755520..94146701..998177623..10637570858

.256.39804.333982.3767186.50742998.670385042.8712117357.113877789805

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 16] for n>18

k=4: [order 64] for n>65

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A302069 A298195 A299089 * A299852 A299008 A299675

Adjacent sequences: A299342 A299343 A299344 * A299346 A299347 A299348

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 07 2018

Status

approved