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A297582 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s.

%I A297582 #4 Jan 01 2018 11:12:14
%S A297582 1,2,1,3,5,1,4,11,9,1,6,17,36,20,1,9,39,72,102,41,1,13,93,188,254,370,
%T A297582 85,1,19,183,688,1017,1104,1243,178,1,28,373,2085,5263,5800,4428,3854,
%U A297582 369,1,41,823,5497,20771,47968,31171,17549,13078,769,1,60,1741,16037,76340
%N A297582 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s.
%C A297582 Table starts
%C A297582 .1...2.....3......4.......6.........9.........13..........19............28
%C A297582 .1...5....11.....17......39........93........183.........373...........823
%C A297582 .1...9....36.....72.....188.......688.......2085........5497.........16037
%C A297582 .1..20...102....254....1017......5263......20771.......76340........320326
%C A297582 .1..41...370...1104....5800.....47968.....284289.....1400065.......8274627
%C A297582 .1..85..1243...4428...31171....395011....3355439....21941552.....181405030
%C A297582 .1.178..3854..17549..171543...3230902...38609160...348140132....4059598106
%C A297582 .1.369.13078..71541..945046..27481626..476513137..5752782514...94310855136
%C A297582 .1.769.43861.288624.5175491.229676841.5731862594.92802629660.2136636243308
%H A297582 R. H. Hardin, <a href="/A297582/b297582.txt">Table of n, a(n) for n = 1..311</a>
%F A297582 Empirical for column k:
%F A297582 k=1: a(n) = a(n-1)
%F A297582 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
%F A297582 k=3: a(n) = a(n-1) +2*a(n-2) +19*a(n-3) +4*a(n-4) -17*a(n-5) -8*a(n-6)
%F A297582 k=4: [order 16]
%F A297582 k=5: [order 30]
%F A297582 k=6: [order 57]
%F A297582 Empirical for row n:
%F A297582 n=1: a(n) = a(n-1) +a(n-3)
%F A297582 n=2: a(n) = a(n-1) +4*a(n-3) +2*a(n-4)
%F A297582 n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +18*a(n-4) +a(n-5) -11*a(n-6) -12*a(n-7) -a(n-8)
%F A297582 n=4: [order 17]
%F A297582 n=5: [order 41]
%F A297582 n=6: [order 94]
%e A297582 Some solutions for n=5 k=4
%e A297582 ..1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
%e A297582 ..0..0..0..0. .0..0..1..0. .1..0..0..0. .0..1..1..0. .0..0..0..0
%e A297582 ..0..0..1..0. .1..1..1..0. .1..0..0..0. .0..1..0..0. .0..1..0..0
%e A297582 ..0..0..0..1. .1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..1..0
%e A297582 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
%Y A297582 Column 2 is A105309(n+1).
%Y A297582 Row 1 is A000930(n+1).
%K A297582 nonn,tabl
%O A297582 1,2
%A A297582 _R. H. Hardin_, Jan 01 2018