login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2018
STATUS
approved