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A280440 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A280440 #4 Jan 03 2017 07:04:51
%S A280440 0,0,0,1,4,1,2,10,10,2,5,20,21,20,5,10,38,42,42,38,10,20,68,77,80,77,
%T A280440 68,20,38,120,136,138,138,136,120,38,71,208,236,232,225,232,236,208,
%U A280440 71,130,358,404,386,360,360,386,404,358,130,235,612,687,640,574,548,574,640,687
%N A280440 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C A280440 Table starts
%C A280440 ...0...0....1....2....5...10...20...38...71..130...235...420...744..1308..2285
%C A280440 ...0...4...10...20...38...68..120..208..358..612..1042..1768..2992..5052..8514
%C A280440 ...1..10...21...42...77..136..236..404..687.1162..1959..3294..5528..9262.15497
%C A280440 ...2..20...42...80..138..232..386..640.1062.1764..2934..4884..8134.13548.22562
%C A280440 ...5..38...77..138..225..360..574..920.1487.2422..3971..6542.10814.17914.29713
%C A280440 ..10..68..136..232..360..548..834.1284.2008.3188..5128..8332.13638.22436.37032
%C A280440 ..20.120..236..386..574..834.1211.1784.2684.4128..6478.10334.16693.27208.44620
%C A280440 ..38.208..404..640..920.1284.1784.2512.3620.5360..8152.12692.20136.32400.52660
%C A280440 ..71.358..687.1062.1487.2008.2684.3620.4989.7078.10365.15642.24224.38290.61451
%C A280440 .130.612.1162.1764.2422.3188.4128.5360.7078.9604.13474.19576.29384.45340.71490
%H A280440 R. H. Hardin, <a href="/A280440/b280440.txt">Table of n, a(n) for n = 1..568</a>
%F A280440 Empirical for column k:
%F A280440 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A280440 k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
%F A280440 k=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>6
%F A280440 k=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
%F A280440 k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
%F A280440 k=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
%F A280440 k=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7
%e A280440 Some solutions for n=4 k=4
%e A280440 ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1
%e A280440 ..0..1..0..1. .1..0..1..1. .1..0..1..0. .1..0..1..0. .0..0..1..0
%e A280440 ..1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..0..1
%e A280440 ..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1. .0..0..1..0
%Y A280440 Column 1 is A001629(n-1).
%Y A280440 Column 2 is A279262.
%K A280440 nonn,tabl
%O A280440 1,5
%A A280440 _R. H. Hardin_, Jan 03 2017