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URL: https://oeis.org/A299682

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A299682
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 45, 45, 73, 32, 64, 157, 147, 211, 147, 157, 64, 128, 353, 506, 1477, 1477, 506, 353, 128, 256, 869, 1561, 7279, 13369, 7279, 1561, 869, 256, 512, 1993, 5017, 35408, 95471, 95471, 35408, 5017, 1993, 512
OFFSET
1,2
COMMENTS
Table starts
...1....2.....4.......8.......16.........32...........64............128
...2....7....13......29.......73........157..........353............869
...4...13....20......45......147........506.........1561...........5017
...8...29....45.....211.....1477.......7279........35408.........196107
..16...73...147....1477....13369......95471.......757628........6503333
..32..157...506....7279....95471....1247427.....16311888......226655504
..64..353..1561...35408...757628...16311888....346275749.....7835688567
.128..869..5017..196107..6503333..226655504...7835688567...289785610230
.256.1993.16429.1040287.52948378.3113437608.174961291252.10547510714203
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
k=3: [order 16] for n>17
k=4: [order 61] for n>64
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0. .0..1..0..0
..0..0..0..1. .1..1..0..1. .0..0..0..1. .1..0..1..0. .1..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..1. .1..0..0..0
..1..0..1..1. .1..0..1..1. .0..1..0..1. .1..0..0..1. .1..0..0..1
..1..0..1..0. .0..1..0..0. .1..1..0..0. .0..0..0..0. .1..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A298215.
Sequence in context: A299879 A299015 A299806 * A300314 A280604 A301323
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 16 2018
STATUS
approved