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.

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

R. H. Hardin, Table of n, a(n) for n = 1..420

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

Adjacent sequences: A298180 A298181 A298182 * A298184 A298185 A298186

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 14 2018

Status

approved