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A316552 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 17, 17, 35, 13, 21, 61, 36, 42, 36, 61, 21, 34, 127, 69, 89, 89, 69, 127, 34, 55, 265, 129, 187, 251, 187, 129, 265, 55, 89, 507, 260, 430, 621, 621, 430, 260, 507, 89, 144, 1013, 544, 1046, 1568, 1811, 1568, 1046, 544 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1...2...3....5.....8....13.....21......34......55.......89.......144

..2...5...7...17....35....61....127.....265.....507.....1013......2071

..3...7..10...17....36....69....129.....260.....544.....1125......2348

..5..17..17...42....89...187....430....1046....2407.....5706.....13873

..8..35..36...89...251...621...1568....4269...11869....33451.....95326

.13..61..69..187...621..1811...5265...17004...54443...174625....570128

.21.127.129..430..1568..5265..18978...73409..276005..1055277...4099795

.34.265.260.1046..4269.17004..73409..336604.1492856..6793881..31252764

.55.507.544.2407.11869.54443.276005.1492856.7870292.42144065.228096346

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..263

FORMULA

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 45] for n>48

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A304221 A305482 A305252 * A316311 A317266 A067330

Adjacent sequences:  A316549 A316550 A316551 * A316553 A316554 A316555

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 06 2018

STATUS

approved

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Last modified May 26 17:49 EDT 2019. Contains 323597 sequences. (Running on oeis4.)