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A316218 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 28, 28, 16, 32, 94, 75, 75, 94, 32, 64, 284, 250, 310, 250, 284, 64, 128, 752, 706, 1468, 1468, 706, 752, 128, 256, 2244, 2116, 5883, 8943, 5883, 2116, 2244, 256, 512, 6532, 6399, 25093, 44018, 44018, 25093, 6399, 6532, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2.....4......8......16.......32.........64.........128..........256

...2....4....14.....28......94......284........752........2244.........6532

...4...14....28.....75.....250......706.......2116........6399........19179

...8...28....75....310....1468.....5883......25093......108869.......463940

..16...94...250...1468....8943....44018.....242149.....1355516......7364630

..32..284...706...5883...44018...273102....1906841....13506787.....92623868

..64..752..2116..25093..242149..1906841...17524746...162191532...1448194529

.128.2244..6399.108869.1355516.13506787..162191532..1966735514..22731828021

.256.6532.19179.463940.7364630.92623868.1448194529.22731828021.338897042438

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>16

k=4: [order 62] for n>64

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A260038 A193916 A304347 * A305642 A317036 A305911

Adjacent sequences:  A316215 A316216 A316217 * A316219 A316220 A316221

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 26 2018

STATUS

approved

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Last modified June 2 10:43 EDT 2020. Contains 334770 sequences. (Running on oeis4.)