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A298183
T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
6
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 3, 3, 5, 0, 0, 8, 5, 6, 6, 5, 8, 0, 0, 13, 8, 10, 15, 10, 8, 13, 0, 0, 21, 13, 15, 27, 27, 15, 13, 21, 0, 0, 34, 21, 26, 54, 53, 54, 26, 21, 34, 0, 0, 55, 34, 44, 117, 114, 114, 117, 44, 34, 55, 0, 0, 89, 55, 71, 237, 257, 231
OFFSET
1,12
COMMENTS
Table starts
.0..0..0..0...0...0....0....0.....0.....0......0......0.......0.......0
.0..1..1..2...3...5....8...13....21....34.....55.....89.....144.....233
.0..1..1..2...3...5....8...13....21....34.....55.....89.....144.....233
.0..2..2..3...6..10...15...26....44....71....118....198.....327.....542
.0..3..3..6..15..27...54..117...237...508...1073...2261....4852...10375
.0..5..5.10..27..53..114..257...561..1286...2875...6483...14836...33739
.0..8..8.15..54.114..231..596..1462..3349...7894..19344...46083..109006
.0.13.13.26.117.257..596.1948..5234.14357..42469.120978..350142.1034253
.0.21.21.44.237.561.1462.5234.15321.48029.155245.482763.1571932.5102212
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +a(n-2)
k=3: a(n) = a(n-1) +a(n-2)
k=4: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) -2*a(n-5)
k=5: [order 10]
k=6: [order 22]
k=7: [order 48]
EXAMPLE
Some solutions for n=7 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
..1..1..1..1. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
CROSSREFS
Column 2 is A000045(n-1).
Column 3 is A000045(n-1).
Sequence in context: A202149 A236533 A298187 * A098356 A298167 A298957
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 14 2018
STATUS
approved