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A298167 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero. 6
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 4, 3, 5, 0, 0, 8, 5, 6, 6, 5, 8, 0, 0, 13, 8, 11, 10, 11, 8, 13, 0, 0, 21, 13, 18, 18, 18, 18, 13, 21, 0, 0, 34, 21, 31, 32, 62, 32, 31, 21, 34, 0, 0, 55, 34, 53, 80, 133, 133, 80, 53, 34, 55, 0, 0, 89, 55, 91, 171, 749, 624 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

Table starts

.0..0..0..0...0....0.....0......0.......0.........0..........0...........0

.0..1..1..2...3....5.....8.....13......21........34.........55..........89

.0..1..1..2...3....5.....8.....13......21........34.........55..........89

.0..2..2..4...6...11....18.....31......53........91........156.........269

.0..3..3..6..10...18....32.....80.....171.......528.......1439........4889

.0..5..5.11..18...62...133....749....2248.....11243......43303......213698

.0..8..8.18..32..133...624...4525...22143....189512....1055639.....8706804

.0.13.13.31..80..749..4525..95458..763536..11467153..117226402..1544912726

.0.21.21.53.171.2248.22143.763536.6564438.187830170.2268628157.49711027609

LINKS

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

FORMULA

Empirical for column k:

k=1: a(n) =

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

k=3: a(n) = a(n-1) +a(n-2)

k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7)

k=5: [order 67]

EXAMPLE

Some solutions for n=8 k=4

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

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

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

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

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

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

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

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

CROSSREFS

Column 2 is A000045(n-1).

Column 3 is A000045(n-1).

Sequence in context: A298187 A298183 A098356 * A298957 A298902 A298963

Adjacent sequences:  A298164 A298165 A298166 * A298168 A298169 A298170

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 14 2018

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)