editing

approved

R. H. Hardin, <a href="/A296386/b296386.txt">Table of n, a(n) for n = 1..337</a>

allocated for R. H. Hardin

T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 2, 4, 10, 4, 7, 28, 28, 7, 12, 86, 127, 86, 12, 21, 279, 641, 641, 279, 21, 37, 869, 3237, 5389, 3237, 869, 37, 65, 2728, 16248, 46786, 46786, 16248, 2728, 65, 114, 8596, 81661, 396806, 684894, 396806, 81661, 8596, 114, 200, 27004, 410199, 3372222

1,2

Table starts

...1.....2.......4.........7..........12............21..............37

...2....10......28........86.........279...........869............2728

...4....28.....127.......641........3237.........16248...........81661

...7....86.....641......5389.......46786........396806.........3372222

..12...279....3237.....46786......684894.......9703136.......138882856

..21...869...16248....396806.....9703136.....229596763......5498685275

..37..2728...81661...3372222...138882856....5498685275....221204933878

..65..8596..410199..28724880..1988460073..131626644289...8887761158698

.114.27004.2061212.244493344.28434977556.3147315906687.356576134627608

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -5*a(n-6) +3*a(n-7) -a(n-8)

k=3: [order 16]

k=4: [order 40]

k=5: [order 92]

Some solutions for n=5 k=4

..0..1..1..0. .0..0..0..0. .1..0..0..1. .0..1..0..1. .0..0..0..1

..0..0..0..0. .0..0..0..1. .1..1..0..1. .1..0..0..1. .0..1..1..0

..0..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..0..0. .1..0..0..0

..0..1..0..1. .1..0..0..0. .0..1..1..0. .0..0..1..1. .1..0..0..0

..0..0..1..0. .1..1..0..0. .1..0..1..1. .0..0..0..0. .1..0..0..0

Column 1 is A005251(n+2).

allocated

nonn,tabl

R. H. Hardin, Dec 11 2017

approved

editing

allocated for R. H. Hardin

allocated

approved