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A297395 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

%I A297395 #4 Dec 29 2017 10:56:51
%S A297395 1,2,1,3,5,1,4,9,9,1,6,13,19,20,1,9,33,37,57,41,1,13,69,127,126,139,
%T A297395 85,1,19,121,323,700,385,369,178,1,28,253,763,2569,3175,1243,963,369,
%U A297395 1,41,529,2121,7779,14940,15541,3924,2489,769,1,60,1013,5557,31081,58901,99682
%N A297395 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.
%C A297395 Table starts
%C A297395 .1...2....3.....4.......6........9........13.........19...........28
%C A297395 .1...5....9....13......33.......69.......121........253..........529
%C A297395 .1...9...19....37.....127......323.......763.......2121.........5557
%C A297395 .1..20...57...126.....700.....2569......7779......31081.......117084
%C A297395 .1..41..139...385....3175....14940.....58901.....325922......1616869
%C A297395 .1..85..369..1243...15541....99682....514945....3977868.....27131403
%C A297395 .1.178..963..3924...74736...640562...4279111...46261441....428200086
%C A297395 .1.369.2489.12477..358341..4101278..35870939..540319235...6780786267
%C A297395 .1.769.6523.39625.1729617.26607999.302197213.6362528482.108762242579
%H A297395 R. H. Hardin, <a href="/A297395/b297395.txt">Table of n, a(n) for n = 1..420</a>
%F A297395 Empirical for column k:
%F A297395 k=1: a(n) = a(n-1)
%F A297395 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
%F A297395 k=3: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -4*a(n-4)
%F A297395 k=4: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -3*a(n-4) -a(n-5) -2*a(n-6) -a(n-7)
%F A297395 k=5: [order 20]
%F A297395 k=6: [order 25]
%F A297395 k=7: [order 55]
%F A297395 Empirical for row n:
%F A297395 n=1: a(n) = a(n-1) +a(n-3)
%F A297395 n=2: a(n) = a(n-1) +4*a(n-3)
%F A297395 n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +a(n-4) -2*a(n-6)
%F A297395 n=4: [order 8]
%F A297395 n=5: [order 21]
%F A297395 n=6: [order 31]
%F A297395 n=7: [order 69]
%e A297395 Some solutions for n=5 k=4
%e A297395 ..0..0..1..1. .0..1..1..0. .0..1..0..0. .0..0..1..1. .0..0..0..0
%e A297395 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0
%e A297395 ..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..1
%e A297395 ..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..0..0
%e A297395 ..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..0..0. .1..0..0..0
%Y A297395 Column 2 is A105309(n+1).
%Y A297395 Row 1 is A000930(n+1).
%Y A297395 Row 2 is A089977(n+1).
%K A297395 nonn,tabl
%O A297395 1,2
%A A297395 _R. H. Hardin_, Dec 29 2017