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.

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

R. H. Hardin, Table of n, a(n) for n = 1..180

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

Adjacent sequences: A303510 A303511 A303512 * A303514 A303515 A303516

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 25 2018

Status

approved