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A299588 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 1, 16, 0, 1, 48, 8, 8, 48, 1, 0, 88, 12, 84, 12, 88, 0, 1, 240, 31, 229, 229, 31, 240, 1, 0, 704, 117, 720, 2170, 720, 117, 704, 0, 1, 1600, 263, 4326, 6418, 6418, 4326, 263, 1600, 1, 0, 4032, 689, 15638, 58139, 38420, 58139, 15638, 689 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

.0....1...0.....1.......0........1..........0............1.............0

.1....4...4....16......48.......88........240..........704..........1600

.0....4...1.....8......12.......31........117..........263...........689

.1...16...8....84.....229......720.......4326........15638.........62867

.0...48..12...229....2170.....6418......58139.......462269.......2322276

.1...88..31...720....6418....38420.....551191......5070055......45637326

.0..240.117..4326...58139...551191...12345692....187346100....2776620332

.1..704.263.15638..462269..5070055..187346100...5383097328..108788947080

.0.1600.689.62867.2322276.45637326.2776620332.108788947080.3979108348246

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

k=3: [order 19] for n>20

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..1..1. .0..0..0..0. .0..1..1..1

..0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..1..1

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1

..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1

..0..0..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1

CROSSREFS

Column 2 is A298448.

Sequence in context: A298622 A298454 A298834 * A299528 A300146 A100045

Adjacent sequences:  A299585 A299586 A299587 * A299589 A299590 A299591

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 13 2018

STATUS

approved

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Last modified January 18 09:12 EST 2022. Contains 350454 sequences. (Running on oeis4.)