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A316383
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 83, 86, 3, 5, 313, 464, 464, 313, 5, 8, 1145, 2280, 3909, 2280, 1145, 8, 13, 4184, 11423, 29877, 29877, 11423, 4184, 13, 21, 15293, 57453, 228485, 353009, 228485, 57453, 15293, 21, 34, 55895, 288496, 1755475, 4067961
OFFSET
1,5
COMMENTS
Table starts
..0.....1.......1.........2..........3............5..............8
..1.....7......23........86........313.........1145...........4184
..1....23......83.......464.......2280........11423..........57453
..2....86.....464......3909......29877.......228485........1755475
..3...313....2280.....29877.....353009......4067961.......47958446
..5..1145...11423....228485....4067961.....70282175.....1244767536
..8..4184...57453...1755475...47958446...1244767536....33482107028
.13.15293..288496..13526926..564507777..22077180053...901574650029
.21.55895.1447883.103864609.6610746658.388558892008.24039453398630
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..0..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..0..1
..1..1..1..1. .0..1..1..0. .0..0..1..0. .1..0..0..1. .1..0..0..1
..1..1..0..1. .1..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1
..0..1..0..0. .0..0..0..1. .1..0..0..1. .0..1..1..0. .0..0..0..0
..0..0..0..1. .1..0..1..0. .1..1..0..1. .1..0..0..0. .0..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A303890.
Sequence in context: A304901 A316583 A304597 * A306143 A317376 A304427
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 30 2018
STATUS
approved