A297094 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s.

2, 4, 4, 8, 15, 8, 16, 45, 45, 16, 32, 152, 228, 152, 32, 64, 511, 1256, 1256, 511, 64, 128, 1681, 6859, 11925, 6859, 1681, 128, 256, 5588, 37423, 113084, 113084, 37423, 5588, 256, 512, 18575, 204625, 1060921, 1850693, 1060921, 204625, 18575, 512, 1024

Offset

1,1

Comments

Table starts

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

...4....15......45.......152..........511...........1681.............5588

...8....45.....228......1256.........6859..........37423...........204625

..16...152....1256.....11925.......113084........1060921.........10038612

..32...511....6859....113084......1850693.......30151640........497994853

..64..1681...37423...1060921.....30151640......859032804......24929815289

.128..5588..204625..10038612....497994853....24929815289....1280846320436

.256.18575.1118722..95094637...8248067202...728501800356...66546097409172

.512.61621.6116809.900615714.136768286476.21357821717826.3477139838772757

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) +3*a(n-3) -14*a(n-4) +4*a(n-5)

k=3: [order 19]

k=4: [order 42]

Example

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

Crossrefs

Column 1 is A000079.

Sequence in context: A240364 A225982 A282528 * A283282 A181253 A267788

Adjacent sequences: A297091 A297092 A297093 * A297095 A297096 A297097

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2017

Status

approved