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A302010 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A302010 #4 Mar 30 2018 12:53:02
%S A302010 1,2,2,4,8,4,8,32,32,8,16,128,240,128,16,32,512,1808,1808,512,32,64,
%T A302010 2048,13616,25808,13616,2048,64,128,8192,102544,369040,368144,102544,
%U A302010 8192,128,256,32768,772272,5276816,9989376,5251712,772272,32768,256,512,131072
%N A302010 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A302010 Table starts
%C A302010 ...1......2........4...........8............16...............32
%C A302010 ...2......8.......32.........128...........512.............2048
%C A302010 ...4.....32......240........1808.........13616...........102544
%C A302010 ...8....128.....1808.......25808........369040..........5276816
%C A302010 ..16....512....13616......368144.......9989376........270990144
%C A302010 ..32...2048...102544.....5251712.....270422672......13918667808
%C A302010 ..64...8192...772272....74917424....7320574992.....714887543376
%C A302010 .128..32768..5816080..1068722240..198174358400...36717919842624
%C A302010 .256.131072.43801648.15245681888.5364752820144.1885898831169344
%H A302010 R. H. Hardin, <a href="/A302010/b302010.txt">Table of n, a(n) for n = 1..479</a>
%F A302010 Empirical for column k:
%F A302010 k=1: a(n) = 2*a(n-1)
%F A302010 k=2: a(n) = 4*a(n-1)
%F A302010 k=3: a(n) = 7*a(n-1) +4*a(n-2)
%F A302010 k=4: a(n) = 13*a(n-1) +18*a(n-2) +a(n-3) -4*a(n-4)
%F A302010 k=5: a(n) = 24*a(n-1) +82*a(n-2) +34*a(n-3) -90*a(n-4) -40*a(n-5) +37*a(n-6)
%F A302010 k=6: [order 10] for n>12
%F A302010 k=7: [order 17] for n>19
%F A302010 Empirical for row n:
%F A302010 n=1: a(n) = 2*a(n-1)
%F A302010 n=2: a(n) = 4*a(n-1)
%F A302010 n=3: a(n) = 7*a(n-1) +4*a(n-2)
%F A302010 n=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4) for n>6
%F A302010 n=5: [order 12] for n>15
%F A302010 n=6: [order 32] for n>36
%F A302010 n=7: [order 78] for n>83
%e A302010 Some solutions for n=5 k=4
%e A302010 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e A302010 ..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..0. .0..0..1..0
%e A302010 ..0..1..0..0. .0..0..1..1. .1..1..1..0. .0..0..1..0. .0..0..0..1
%e A302010 ..1..1..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .1..1..0..1
%e A302010 ..0..1..0..1. .0..0..1..0. .0..1..0..0. .1..1..1..0. .0..0..0..0
%Y A302010 Column 1 and row 1 are A000079(n-1).
%Y A302010 Column 2 and row 2 are A004171(n-1).
%Y A302010 Column 3 and row 3 are A301779.
%K A302010 nonn,tabl
%O A302010 1,2
%A A302010 _R. H. Hardin_, Mar 30 2018