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A316883 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 37, 28, 16, 32, 94, 105, 105, 94, 32, 64, 284, 388, 452, 388, 284, 64, 128, 752, 1280, 2401, 2401, 1280, 752, 128, 256, 2244, 4121, 11532, 18847, 11532, 4121, 2244, 256, 512, 6532, 13933, 54613, 125218, 125218, 54613 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

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

...4...14....37.....105......388.......1280........4121.........13933

...8...28...105.....452.....2401......11532.......54613........268142

..16...94...388....2401....18847.....125218......843479.......6198339

..32..284..1280...11532...125218....1187727....11791971.....128278641

..64..752..4121...54613...843479...11791971...180224021....3018929955

.128.2244.13933..268142..6198339..128278641..3018929955...79732305036

.256.6532.46641.1322178.45184963.1404259002.51534776482.2144543383081

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

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>17

k=4: [order 61] for n>63

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A317036 A305911 A317153 * A317611 A220461 A220287

Adjacent sequences:  A316880 A316881 A316882 * A316884 A316885 A316886

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 15 2018

STATUS

approved

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Last modified October 18 13:21 EDT 2021. Contains 348067 sequences. (Running on oeis4.)