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A303456
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 232, 128, 16, 32, 512, 1690, 1696, 512, 32, 64, 2048, 12340, 22756, 12408, 2048, 64, 128, 8192, 90112, 306448, 306767, 90800, 8192, 128, 256, 32768, 658204, 4129588, 7626768, 4136339, 664512, 32768, 256, 512, 131072
OFFSET
1,2
COMMENTS
Table starts
...1......2........4...........8............16..............32
...2......8.......32.........128...........512............2048
...4.....32......232........1690.........12340...........90112
...8....128.....1696.......22756........306448.........4129588
..16....512....12408......306767.......7626768.......189848373
..32...2048....90800.....4136339.....189837638......8727953509
..64...8192...664512....55781418....4726484016....401405461699
.128..32768..4863312...752277525..117683035940..18461936404456
.256.131072.35593024.10145443043.2930192820802.849140799884830
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -4*a(n-2) -2*a(n-3) -36*a(n-4) -16*a(n-5)
k=4: [order 15]
k=5: [order 47]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1)
n=3: a(n) = 8*a(n-1) -40*a(n-3) +20*a(n-4) +8*a(n-5) -3*a(n-6) +32*a(n-7) for n>8
n=4: [order 15] for n>16
n=5: [order 68] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..1
..1..1..1..0. .1..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
..0..0..1..1. .0..1..0..1. .1..0..0..0. .1..1..1..0. .0..0..1..1
..0..1..1..0. .0..1..0..0. .1..1..1..1. .0..1..1..0. .0..0..0..1
..0..0..0..1. .0..0..1..1. .1..1..0..1. .0..0..1..1. .0..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A004171(n-1).
Sequence in context: A302741 A300215 A300804 * A301443 A302010 A301784
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 24 2018
STATUS
approved