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A300267
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6, 7 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, 1526, 2030, 1526, 1012, 64, 128, 3440, 6198, 12324, 12324, 6198, 3440, 128, 256, 11700, 25034, 71529, 138215, 71529, 25034, 11700, 256, 512, 39804, 101312, 412094
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.......1526........6198.........25034..........101312
...8....88....375.....2030......12324.......71529........412094.........2398145
..16...298...1526....12324.....138215.....1333242......12622937.......125646087
..32..1012...6198....71529....1333242....20341795.....298472434......4660242199
..64..3440..25034...412094...12622937...298472434....6717267728....162737578821
.128.11700.101312..2398145..125646087..4660242199..162737578821...6293324571337
.256.39804.410252.13965762.1244747820.72718129316.3942079842968.243019177909127
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 64] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..0. .0..1..1..1
..1..0..1..1. .0..0..0..0. .0..0..0..1. .1..0..1..0. .0..1..1..1
..1..0..0..1. .1..1..1..1. .1..0..1..1. .0..0..1..0. .0..1..1..1
..0..1..1..0. .0..0..0..1. .1..0..0..1. .1..0..1..1. .0..0..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298189.
Sequence in context: A299008 A299675 A299753 * A318016 A320402 A208709
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2018
STATUS
approved