A297682 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

2, 4, 4, 7, 11, 8, 13, 29, 33, 16, 24, 80, 150, 98, 32, 44, 219, 629, 742, 291, 64, 81, 597, 2790, 4633, 3744, 865, 128, 149, 1632, 12110, 32911, 34872, 18840, 2570, 256, 274, 4459, 52889, 221420, 401678, 260924, 94891, 7637, 512, 504, 12181, 230406, 1519630

Offset

1,1

Comments

Table starts

...2.....4.......7........13.........24...........44.............81

...4....11......29........80........219..........597...........1632

...8....33.....150.......629.......2790........12110..........52889

..16....98.....742......4633......32911.......221420........1519630

..32...291....3744.....34872.....401678......4202440.......45865837

..64...865...18840....260924....4870764.....78957968.....1368968852

.128..2570...94891...1955750...59210634...1487819051....41030621948

.256..7637..477850..14651847..719647644..28013761161..1229127412701

.512.22693.2406649.109783269.8748946600.527589764007.36837288191422

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)

k=3: a(n) = 5*a(n-1) -a(n-2) +8*a(n-3) -5*a(n-4) -30*a(n-5) +17*a(n-6)

k=4: [order 16]

k=5: [order 30]

k=6: [order 57]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2) +a(n-3)

n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4)

n=3: [order 8]

n=4: [order 17]

n=5: [order 41]

Example

Some solutions for n=4 k=4
..0..1..0..1. .1..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
..0..0..1..1. .0..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..0
..0..1..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..1. .0..0..0..0
..0..1..0..0. .1..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..1

Crossrefs

Column 1 is A000079.

Column 2 is A282990.

Row 1 is A000073(n+3).

Row 2 is A124861(n+1).

Sequence in context: A295652 A269075 A283543 * A297607 A223770 A223777

Adjacent sequences: A297679 A297680 A297681 * A297683 A297684 A297685

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2018

Status

approved