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A298501 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 1, 13, 8, 13, 34, 4, 4, 34, 13, 21, 73, 5, 38, 5, 73, 21, 34, 203, 6, 54, 54, 6, 203, 34, 55, 594, 20, 97, 281, 97, 20, 594, 55, 89, 1443, 35, 467, 403, 403, 467, 35, 1443, 89, 144, 4013, 70, 1105, 2353, 277, 2353, 1105, 70, 4013, 144, 233 (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....4..3...13....34....73....203.....594.....1443......4013......11114

..3....3..1....4.....5.....6.....20......35.......70.......174........365

..5...13..4...38....54....97....467....1105.....3354.....12283......37107

..8...34..5...54...281...403...2353...12942....43319....219059....1139692

.13...73..6...97...403...277...1602....6037....19001.....93205.....385257

.21..203.20..467..2353..1602..24272..118439...372820...3857775...22638601

.34..594.35.1105.12942..6037.118439.1377101..4336887..60191437..664833900

.55.1443.70.3354.43319.19001.372820.4336887.10659243.151971896.1550220630

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

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 15] for n>16

k=4: [order 51] for n>54

EXAMPLE

Some solutions for n=6 k=4

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A297901.

Sequence in context: A047675 A187199 A297907 * A298320 A299393 A299194

Adjacent sequences:  A298498 A298499 A298500 * A298502 A298503 A298504

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 20 2018

STATUS

approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)