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A316455 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 9, 10, 3, 5, 51, 23, 23, 51, 5, 8, 165, 58, 48, 58, 165, 8, 13, 306, 126, 229, 229, 126, 306, 13, 21, 993, 272, 850, 1591, 850, 272, 993, 21, 34, 2867, 672, 3223, 6590, 6590, 3223, 672, 2867, 34, 55, 6818, 1553, 10880, 29406, 53863 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0....1....1.....2.......3........5.........8..........13...........21

..1....3...11....10......51......165.......306.........993.........2867

..1...11....9....23......58......126.......272.........672.........1553

..2...10...23....48.....229......850......3223.......10880........45692

..3...51...58...229....1591.....6590.....29406......180787......1110885

..5..165..126...850....6590....53863....349456.....3164734.....29901503

..8..306..272..3223...29406...349456...4145337....44700278....711845805

.13..993..672.10880..180787..3164734..44700278...935229204..23033473439

.21.2867.1553.45692.1110885.29901503.711845805.23033473439.873192441329

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 17] for n>20

k=4: [order 67] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A304058 A305452 A304704 * A305015 A316648 A316176

Adjacent sequences:  A316452 A316453 A316454 * A316456 A316457 A316458

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 03 2018

STATUS

approved

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Last modified September 20 03:55 EDT 2019. Contains 327212 sequences. (Running on oeis4.)