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A305252 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 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, 34, 42, 34, 61, 21, 34, 127, 65, 79, 79, 65, 127, 34, 55, 265, 121, 163, 203, 163, 121, 265, 55, 89, 507, 244, 356, 439, 439, 356, 244, 507, 89, 144, 1013, 502, 794, 1010, 1149, 1010, 794, 502, 1013 (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.......233

..2...5...7...17...35....61...127....265.....507....1013.....2071......4097

..3...7..10...17...34....65...121....244.....502....1023.....2112......4430

..5..17..17...42...79...163...356....794....1699....3824.....8679.....19781

..8..35..34...79..203...439..1010...2382....5699...13811....33747.....82601

.13..61..65..163..439..1149..2985...8254...22801...62473...173206....483696

.21.127.121..356.1010..2985..9288..29714...94491..302488...974340...3152830

.34.265.244..794.2382..8254.29714.110121..399364.1469285..5435109..20207222

.55.507.502.1699.5699.22801.94491.399364.1688401.7171215.30542434.130768430

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..312

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 12]

k=4: [order 26] for n>30

k=5: [order 54] for n>59

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A306129 A304221 A305482 * A316552 A316311 A317266

Adjacent sequences:  A305249 A305250 A305251 * A305253 A305254 A305255

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 28 2018

STATUS

approved

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Last modified May 19 17:48 EDT 2019. Contains 323395 sequences. (Running on oeis4.)