A317383 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 18, 9, 16, 32, 22, 36, 36, 22, 32, 64, 45, 94, 123, 94, 45, 64, 128, 101, 270, 414, 414, 270, 101, 128, 256, 218, 731, 1580, 2089, 1580, 731, 218, 256, 512, 477, 1973, 5704, 10732, 10732, 5704, 1973, 477, 512, 1024, 1041, 5388

Offset

1,2

Comments

Table starts

...1...2....4.....8......16.......32........64........128..........256

...2...4....5.....9......22.......45.......101........218..........477

...4...5...18....36......94......270.......731.......1973.........5388

...8...9...36...123.....414.....1580......5704......20162........72715

..16..22...94...414....2089....10732.....52617.....260141......1299431

..32..45..270..1580...10732....75405....508181....3446847.....23624322

..64.101..731..5704...52617...508181...4726521...44156330....416173164

.128.218.1973.20162..260141..3446847..44156330..569899203...7400913778

.256.477.5388.72715.1299431.23624322.416173164.7400913778.132364711390

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6

k=3: a(n) = a(n-1) +3*a(n-2) +5*a(n-3) +2*a(n-4) -3*a(n-5) -10*a(n-6) -8*a(n-7) for n>10

k=4: [order 19] for n>23

k=5: [order 43] for n>49

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A316420 A304926 A306166 * A033717 A320202 A320201

Adjacent sequences: A317380 A317381 A317382 * A317384 A317385 A317386

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 26 2018

Status

approved