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A316648 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 15, 10, 3, 5, 51, 33, 33, 51, 5, 8, 165, 117, 42, 117, 165, 8, 13, 306, 247, 277, 277, 247, 306, 13, 21, 993, 599, 954, 3988, 954, 599, 993, 21, 34, 2867, 1757, 2432, 13869, 13869, 2432, 1757, 2867, 34, 55, 6818, 4241, 10541, 54941 (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...15....33.....117.....247.......599.......1757........4241

..2...10...33....42.....277.....954......2432......10541.......39013

..3...51..117...277....3988...13869.....54941.....427096.....1946889

..5..165..247...954...13869...43604....228056....1976020.....9093873

..8..306..599..2432...54941..228056...1396674...17049299...106043303

.13..993.1757.10541..427096.1976020..17049299..331807728..2594184863

.21.2867.4241.39013.1946889.9093873.106043303.2594184863.22368384180

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

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]

k=4: [order 69] for n>70

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304052.

Sequence in context: A304704 A316455 A305015 * A316176 A317458 A301615

Adjacent sequences:  A316645 A316646 A316647 * A316649 A316650 A316651

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 09 2018

STATUS

approved

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)