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A316822 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 169, 112, 16, 32, 420, 983, 983, 420, 32, 64, 1576, 5701, 9233, 5701, 1576, 64, 128, 5912, 33046, 87009, 87009, 33046, 5912, 128, 256, 22176, 191692, 811854, 1363249, 811854, 191692, 22176, 256, 512, 83184, 1111756 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2.....8......30.......112.........420..........1576............5912

...4....30.....169.......983........5701.........33046..........191692

...8...112.....983......9233.......87009........811854.........7609680

..16...420....5701.....87009.....1363249......20825877.......321003969

..32..1576...33046....811854....20825877.....513913591.....12835573991

..64..5912..191692...7609680...321003969...12835573991....521608116975

.128.22176.1111756..71307863..4949107992..320914969638..21245308955509

.256.83184.6447926.667818686.76181954073.8003158157235.862069068522225

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) = 4*a(n-1) -2*a(n-2) +4*a(n-3)

k=3: [order 11] for n>12

k=4: [order 38] for n>39

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A281949.

Sequence in context: A317118 A305530 A317004 * A317572 A281837 A299081

Adjacent sequences:  A316819 A316820 A316821 * A316823 A316824 A316825

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 14 2018

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)