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A316822
T(n,k) = Number of n X k 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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 14 2018
STATUS
approved