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A283042 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

%I A283042 #4 Feb 27 2017 09:01:44
%S A283042 0,0,0,1,4,1,2,16,16,2,5,68,119,68,5,12,256,818,818,256,12,26,924,
%T A283042 5065,9152,5065,924,26,56,3232,30378,94368,94368,30378,3232,56,118,
%U A283042 11044,175963,931844,1604067,931844,175963,11044,118,244,37104,997302,8912378
%N A283042 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.
%C A283042 Table starts
%C A283042 ...0......0........1..........2.............5..............12................26
%C A283042 ...0......4.......16.........68...........256.............924..............3232
%C A283042 ...1.....16......119........818..........5065...........30378............175963
%C A283042 ...2.....68......818.......9152.........94368..........931844...........8912378
%C A283042 ...5....256.....5065......94368.......1604067........26180826.........414085368
%C A283042 ..12....924....30378.....931844......26180826.......706205768.......18455711930
%C A283042 ..26...3232...175963....8912378.....414085368.....18455711930......797350288363
%C A283042 ..56..11044...997302...83420984....6406597648....471954803540....33705434438284
%C A283042 .118..37104..5559013..767704036...97480211225..11868995624930..1401215705047092
%C A283042 .244.122984.30578068.6973000128.1463896864692.294610925837548.57496998569457406
%H A283042 R. H. Hardin, <a href="/A283042/b283042.txt">Table of n, a(n) for n = 1..220</a>
%F A283042 Empirical for column k:
%F A283042 k=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
%F A283042 k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)
%F A283042 k=3: [order 18]
%F A283042 k=4: [order 30]
%F A283042 k=5: [order 72]
%e A283042 Some solutions for n=4 k=4
%e A283042 ..0..0..1..0. .1..0..0..0. .1..0..1..0. .0..0..1..1. .1..0..0..1
%e A283042 ..1..0..1..0. .1..1..0..0. .0..1..1..1. .0..1..0..0. .0..1..0..1
%e A283042 ..0..0..1..0. .0..0..1..0. .1..0..1..0. .1..0..1..0. .0..1..0..1
%e A283042 ..1..0..0..0. .1..0..1..0. .1..0..0..0. .1..1..0..0. .0..0..0..0
%Y A283042 Column 1 is A073778(n-1).
%K A283042 nonn,tabl
%O A283042 1,5
%A A283042 _R. H. Hardin_, Feb 27 2017