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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.

%I A297682 #4 Jan 03 2018 09:29:31
%S A297682 2,4,4,7,11,8,13,29,33,16,24,80,150,98,32,44,219,629,742,291,64,81,
%T A297682 597,2790,4633,3744,865,128,149,1632,12110,32911,34872,18840,2570,256,
%U A297682 274,4459,52889,221420,401678,260924,94891,7637,512,504,12181,230406,1519630
%N 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.
%C A297682 Table starts
%C A297682 ...2.....4.......7........13.........24...........44.............81
%C A297682 ...4....11......29........80........219..........597...........1632
%C A297682 ...8....33.....150.......629.......2790........12110..........52889
%C A297682 ..16....98.....742......4633......32911.......221420........1519630
%C A297682 ..32...291....3744.....34872.....401678......4202440.......45865837
%C A297682 ..64...865...18840....260924....4870764.....78957968.....1368968852
%C A297682 .128..2570...94891...1955750...59210634...1487819051....41030621948
%C A297682 .256..7637..477850..14651847..719647644..28013761161..1229127412701
%C A297682 .512.22693.2406649.109783269.8748946600.527589764007.36837288191422
%H A297682 R. H. Hardin, <a href="/A297682/b297682.txt">Table of n, a(n) for n = 1..287</a>
%F A297682 Empirical for column k:
%F A297682 k=1: a(n) = 2*a(n-1)
%F A297682 k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
%F A297682 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 A297682 k=4: [order 16]
%F A297682 k=5: [order 30]
%F A297682 k=6: [order 57]
%F A297682 Empirical for row n:
%F A297682 n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F A297682 n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4)
%F A297682 n=3: [order 8]
%F A297682 n=4: [order 17]
%F A297682 n=5: [order 41]
%e A297682 Some solutions for n=4 k=4
%e A297682 ..0..1..0..1. .1..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
%e A297682 ..0..0..1..1. .0..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..0
%e A297682 ..0..1..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..1. .0..0..0..0
%e A297682 ..0..1..0..0. .1..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..1
%Y A297682 Column 1 is A000079.
%Y A297682 Column 2 is A282990.
%Y A297682 Row 1 is A000073(n+3).
%Y A297682 Row 2 is A124861(n+1).
%K A297682 nonn,tabl
%O A297682 1,1
%A A297682 _R. H. Hardin_, Jan 03 2018