|
%I #4 Jan 03 2017 07:04:51
%S 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 68,20,38,120,136,138,138,136,120,38,71,208,236,232,225,232,236,208,
%U 71,130,358,404,386,360,360,386,404,358,130,235,612,687,640,574,548,574,640,687
%N 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 Table starts
%C ...0...0....1....2....5...10...20...38...71..130...235...420...744..1308..2285
%C ...0...4...10...20...38...68..120..208..358..612..1042..1768..2992..5052..8514
%C ...1..10...21...42...77..136..236..404..687.1162..1959..3294..5528..9262.15497
%C ...2..20...42...80..138..232..386..640.1062.1764..2934..4884..8134.13548.22562
%C ...5..38...77..138..225..360..574..920.1487.2422..3971..6542.10814.17914.29713
%C ..10..68..136..232..360..548..834.1284.2008.3188..5128..8332.13638.22436.37032
%C ..20.120..236..386..574..834.1211.1784.2684.4128..6478.10334.16693.27208.44620
%C ..38.208..404..640..920.1284.1784.2512.3620.5360..8152.12692.20136.32400.52660
%C ..71.358..687.1062.1487.2008.2684.3620.4989.7078.10365.15642.24224.38290.61451
%C .130.612.1162.1764.2422.3188.4128.5360.7078.9604.13474.19576.29384.45340.71490
%H R. H. Hardin, <a href="/A280440/b280440.txt">Table of n, a(n) for n = 1..568</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
%F 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 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 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 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 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 Some solutions for n=4 k=4
%e ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..1..0..1
%e ..0..1..0..1. .1..0..1..1. .1..0..1..0. .1..0..1..0. .0..0..1..0
%e ..1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..0..1
%e ..1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1. .0..0..1..0
%Y Column 1 is A001629(n-1).
%Y Column 2 is A279262.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 03 2017
| 