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A303325 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303325 #4 Apr 21 2018 13:13:44
%S A303325 1,1,2,1,2,4,1,8,1,8,1,8,4,2,16,1,32,1,8,1,32,1,32,4,2,16,2,64,1,128,
%T A303325 1,12,4,32,1,128,1,128,4,10,64,3,64,2,256,1,512,1,46,25,62,3,128,1,
%U A303325 512,1,512,4,50,368,56,204,10,256,2,1024,1,2048,1,204,201,758,136,744,9,512,1
%N A303325 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303325 Table starts
%C A303325 ...1.1...1..1...1....1.....1.....1.......1........1.........1..........1
%C A303325 ...2.2...8..8..32...32...128...128.....512......512......2048.......2048
%C A303325 ...4.1...4..1...4....1.....4.....1.......4........1.........4..........1
%C A303325 ...8.2...8..2..12...10....46....50.....204......290......1034.......1682
%C A303325 ..16.1..16..4..64...25...368...201....2545.....1855.....21082......17922
%C A303325 ..32.2..32..3..62...56...758...822...11950....15100....206189.....274746
%C A303325 ..64.1..64..3.204..136..2956..3929...69328...130531...2005898....4227664
%C A303325 .128.2.128.10.744..531.15494.24759..629227..1489177..33766564...89782726
%C A303325 .256.1.256..9.900.1035.44101.97205.3531980.11297739.359263250.1265799068
%H A303325 R. H. Hardin, <a href="/A303325/b303325.txt">Table of n, a(n) for n = 1..242</a>
%F A303325 Empirical for column k:
%F A303325 k=1: a(n) = 2*a(n-1)
%F A303325 k=2: a(n) = a(n-2)
%F A303325 k=3: a(n) = 2*a(n-1) for n>3
%F A303325 k=4: [order 55] for n>57
%F A303325 k=5: [order 33] for n>35
%F A303325 Empirical for row n:
%F A303325 n=1: a(n) = a(n-1)
%F A303325 n=2: a(n) = 4*a(n-2)
%F A303325 n=3: a(n) = a(n-2)
%F A303325 n=4: [order 18] for n>19
%F A303325 n=5: [order 34] for n>35
%e A303325 All solutions for n=5 k=4
%e A303325 ..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
%e A303325 ..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
%e A303325 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A303325 ..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
%e A303325 ..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
%Y A303325 Column 1 is A000079(n-1).
%Y A303325 Column 3 is A000079(n-1) for n>2.
%Y A303325 Row 2 is A158302(n+1).
%Y A303325 Row 3 is A010685(n+8).
%K A303325 nonn,tabl
%O A303325 1,3
%A A303325 _R. H. Hardin_, Apr 21 2018