A297682 - OEIS

%I #4 Jan 03 2018 09:29:31

%S 2,4,4,7,11,8,13,29,33,16,24,80,150,98,32,44,219,629,742,291,64,81,

%T 597,2790,4633,3744,865,128,149,1632,12110,32911,34872,18840,2570,256,

%U 274,4459,52889,221420,401678,260924,94891,7637,512,504,12181,230406,1519630

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

%C Table starts

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

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

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

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

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

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

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

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

%C .512.22693.2406649.109783269.8748946600.527589764007.36837288191422

%H R. H. Hardin, <a href="/A297682/b297682.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

%F 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)

%F k=4: [order 16]

%F k=5: [order 30]

%F k=6: [order 57]

%F Empirical for row n:

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

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

%F n=3: [order 8]

%F n=4: [order 17]

%F n=5: [order 41]

%e Some solutions for n=4 k=4

%e ..0..1..0..1. .1..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0

%e ..0..0..1..1. .0..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..0

%e ..0..1..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..1. .0..0..0..0

%e ..0..1..0..0. .1..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..1

%Y Column 1 is A000079.

%Y Column 2 is A282990.

%Y Row 1 is A000073(n+3).

%Y Row 2 is A124861(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 03 2018