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A304597
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 82, 86, 3, 5, 313, 456, 456, 313, 5, 8, 1145, 2207, 3789, 2207, 1145, 8, 13, 4184, 10949, 28251, 28251, 10949, 4184, 13, 21, 15293, 54357, 211833, 316549, 211833, 54357, 15293, 21, 34, 55895, 269732, 1593375, 3512756
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1........2..........3............5..............8
..1.....7......23.......86........313.........1145...........4184
..1....23......82......456.......2207........10949..........54357
..2....86.....456.....3789......28251.......211833........1593375
..3...313....2207....28251.....316549......3512756.......39628005
..5..1145...10949...211833....3512756.....57480334......957716506
..8..4184...54357..1593375...39628005....957716506....23762003978
.13.15293..269732.12018566..447041946..15998181972...591616446858
.21.55895.1337127.90361561.5016259480.265138740428.14572206851838
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
k=3: [order 15] for n>16
k=4: [order 50] for n>51
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..0..1. .0..0..0..1
..0..0..1..1. .0..0..1..0. .1..1..0..1. .1..0..1..1. .0..1..1..0
..0..0..1..0. .1..1..1..0. .1..0..0..0. .1..1..1..1. .1..1..1..0
..1..0..0..0. .1..1..1..1. .1..0..0..1. .0..1..0..1. .0..1..1..0
..1..1..0..1. .0..1..0..0. .1..0..0..1. .1..0..0..1. .0..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A303890.
Sequence in context: A305288 A304901 A316583 * A316383 A306143 A317376
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 15 2018
STATUS
approved