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A299345
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 93, 88, 16, 32, 298, 357, 357, 298, 32, 64, 1012, 1399, 1618, 1399, 1012, 64, 128, 3440, 5513, 7667, 7667, 5513, 3440, 128, 256, 11700, 21642, 36182, 45287, 36182, 21642, 11700, 256, 512, 39804, 85000, 170056, 262230, 262230
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2......4.......8.......16........32.........64..........128
...2.....8.....26......88......298......1012.......3440........11700
...4....26.....93.....357.....1399......5513......21642........85000
...8....88....357....1618.....7667.....36182.....170056.......800122
..16...298...1399....7667....45287....262230....1511085......8755520
..32..1012...5513...36182...262230...1870946...13239850.....94146701
..64..3440..21642..170056..1511085..13239850..114730926....998177623
.128.11700..85000..800122..8755520..94146701..998177623..10637570858
.256.39804.333982.3767186.50742998.670385042.8712117357.113877789805
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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FORMULA
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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 16] for n>18
k=4: [order 64] for n>65
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .1..1..1..1
..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..1..1..1. .1..1..1..1
..1..1..1..1. .0..0..0..1. .0..1..0..1. .0..1..1..1. .1..1..1..1
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A298189.
Sequence in context: A302069 A298195 A299089 * A299852 A299008 A299675
Adjacent sequences: A299342 A299343 A299344 * A299346 A299347 A299348
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 07 2018
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STATUS
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approved
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