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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)