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A299753
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 95, 88, 16, 32, 298, 375, 375, 298, 32, 64, 1012, 1524, 1998, 1524, 1012, 64, 128, 3440, 6170, 11733, 11733, 6170, 3440, 128, 256, 11700, 24838, 64703, 115279, 64703, 24838, 11700, 256, 512, 39804, 100272, 358219, 915181
OFFSET
1,2
COMMENTS
Table starts
...1.....2......4........8........16..........32...........64............128
...2.....8.....26.......88.......298........1012.........3440..........11700
...4....26.....95......375......1524........6170........24838.........100272
...8....88....375.....1998.....11733.......64703.......358219........2010841
..16...298...1524....11733....115279......915181......7443583.......65049552
..32..1012...6170....64703....915181.....9822603....109073249.....1317338135
..64..3440..24838...358219...7443583...109073249...1686794332....28696396155
.128.11700.100272..2010841..65049552..1317338135..28696396155...723176599097
.256.39804.405068.11248655.548247606.15245980679.463029637815.16724897634952
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) +2*a(n-3) -6*a(n-4) -4*a(n-5)
k=3: [order 18] for n>19
k=4: [order 65] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..1..1..1. .0..0..0..1. .0..0..0..0
..0..1..0..0. .0..0..0..0. .1..0..0..1. .1..0..1..0. .1..1..0..1
..0..0..1..1. .1..1..1..1. .1..0..1..0. .1..0..0..0. .1..0..1..0
..0..1..0..0. .0..1..0..0. .0..1..1..0. .1..1..0..1. .0..1..1..1
..0..1..1..1. .1..1..0..1. .1..0..1..0. .0..0..0..0. .1..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298189.
Sequence in context: A299852 A299008 A299675 * A300267 A318016 A320402
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 18 2018
STATUS
approved