login
A297094
T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s.
8
2, 4, 4, 8, 15, 8, 16, 45, 45, 16, 32, 152, 228, 152, 32, 64, 511, 1256, 1256, 511, 64, 128, 1681, 6859, 11925, 6859, 1681, 128, 256, 5588, 37423, 113084, 113084, 37423, 5588, 256, 512, 18575, 204625, 1060921, 1850693, 1060921, 204625, 18575, 512, 1024
OFFSET
1,1
COMMENTS
Table starts
...2.....4.......8........16...........32.............64..............128
...4....15......45.......152..........511...........1681.............5588
...8....45.....228......1256.........6859..........37423...........204625
..16...152....1256.....11925.......113084........1060921.........10038612
..32...511....6859....113084......1850693.......30151640........497994853
..64..1681...37423...1060921.....30151640......859032804......24929815289
.128..5588..204625..10038612....497994853....24929815289....1280846320436
.256.18575.1118722..95094637...8248067202...728501800356...66546097409172
.512.61621.6116809.900615714.136768286476.21357821717826.3477139838772757
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +3*a(n-3) -14*a(n-4) +4*a(n-5)
k=3: [order 19]
k=4: [order 42]
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..1. .1..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..1..0
..0..1..0..0. .0..0..0..0. .0..0..0..0. .1..0..1..0. .0..0..0..0
..0..0..1..0. .1..0..0..0. .0..0..1..0. .0..0..0..1. .1..0..0..0
..0..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..1..0. .1..0..0..1
CROSSREFS
Column 1 is A000079.
Sequence in context: A240364 A225982 A282528 * A283282 A181253 A267788
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 25 2017
STATUS
approved