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A298177
T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.
4
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 8, 2, 2, 8, 0, 0, 5, 1, 8, 1, 5, 0, 0, 22, 6, 13, 13, 6, 22, 0, 0, 29, 8, 27, 34, 27, 8, 29, 0, 0, 60, 15, 43, 57, 57, 43, 15, 60, 0, 0, 121, 22, 104, 73, 87, 73, 104, 22, 121, 0, 0, 194, 44, 220, 174, 161, 161, 174, 220, 44, 194, 0, 0, 425, 82
OFFSET
1,8
COMMENTS
Table starts
.0..0..0...0...0...0....0....0....0.....0.....0.....0......0......0......0
.0..1..2...1...8...5...22...29...60...121...194...425....704...1421...2574
.0..2..0...2...1...6....8...15...22....44....82...152....267....486....898
.0..1..2...8..13..27...43..104..220...478...988..2085...4451...9505..20311
.0..8..1..13..34..57...73..174..350...800..1605..3376...7079..15234..32785
.0..5..6..27..57..87..161..361..898..1984..4089..8938..20136..45253.100907
.0.22..8..43..73.161..181..540.1076..2572..5179.11814..27638..63592.145715
.0.29.15.104.174.361..540.1380.2682..6043.12820.28413..61050.133945.294724
.0.60.22.220.350.898.1076.2682.4176.11358.21477.51492.105048.245900.540109
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4)
k=3: a(n) = a(n-1) +2*a(n-2) +2*a(n-5) -4*a(n-6) -8*a(n-7) -a(n-8) +a(n-9)
k=4: [order 21] for n>27
k=5: [order 34] for n>40
k=6: [order 67] for n>74
EXAMPLE
Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..1..0..1. .1..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..1
..0..1..0..1. .1..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..0
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..0
..0..1..0..1. .1..0..0..1. .1..0..1..0. .0..1..1..0. .0..1..1..0
..0..0..1..1. .1..1..1..1. .1..1..0..0. .0..0..0..0. .0..0..0..0
CROSSREFS
Column 2 is A297809.
Column 3 is A298141.
Column 4 is A298142.
Column 5 is A298143.
Sequence in context: A141612 A316342 A297814 * A298146 A295520 A295335
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 14 2018
STATUS
approved