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A303513
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 78, 81, 16, 32, 136, 230, 420, 264, 32, 64, 360, 801, 1596, 2088, 857, 64, 128, 960, 2764, 7951, 10128, 9916, 2785, 128, 256, 2576, 9367, 43448, 72890, 59086, 49740, 9050, 256, 512, 6944, 31703, 222205, 656838, 613788
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4........8........16..........32............64............128
...2.....8......20.......52.......136.........360...........960...........2576
...4....25......78......230.......801........2764..........9367..........31703
...8....81.....420.....1596......7951.......43448........222205........1111647
..16...264....2088....10128.....72890......656838.......5122419.......37600463
..32...857....9916....59086....613788.....8883058.....104285205.....1111578890
..64..2785...49740...377020...5520182...130480638....2346396384....36337215370
.128..9050..245904..2366996..49761178..1939853204...53305999504..1203039901394
.256.29407.1204720.14512973.438900203.28081434251.1176790967846.38683326206589
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 49] for n>51
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) for n>4
n=3: [order 15] for n>16
n=4: [order 63] for n>65
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..1
..0..1..1..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .0..0..1..0
..1..1..1..0. .1..1..1..0. .1..1..1..0. .1..0..0..1. .0..1..0..1
..1..0..1..0. .0..0..1..1. .1..0..0..0. .0..1..1..1. .0..1..1..1
..1..0..0..0. .1..1..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240478.
Row 1 is A000079(n-1).
Row 2 is A302323.
Sequence in context: A302322 A303016 A302820 * A303727 A305230 A304775
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 25 2018
STATUS
approved