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A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A302069 #4 Mar 31 2018 15:45:01
%S A302069 1,2,2,4,8,4,8,25,32,8,16,81,148,128,16,32,263,748,884,512,32,64,855,
%T A302069 3657,7070,5296,2048,64,128,2778,18108,54177,67070,31760,8192,128,256,
%U A302069 9027,89658,420121,807601,636852,190528,32768,256,512,29333,444359
%N A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A302069 Table starts
%C A302069 ...1......2.......4.........8..........16............32..............64
%C A302069 ...2......8......25........81.........263...........855............2778
%C A302069 ...4.....32.....148.......748........3657.........18108...........89658
%C A302069 ...8....128.....884......7070.......54177........420121.........3247765
%C A302069 ..16....512....5296.....67070......807601.......9825815.......119508742
%C A302069 ..32...2048...31760....636852....12063625.....230634314......4418931065
%C A302069 ..64...8192..190528...6048836...180330117....5420105343....163660519064
%C A302069 .128..32768.1143104..57457232..2696254757..127431664603...6065045335103
%C A302069 .256.131072.6858496.545796112.40316943551.2996509042607.224815724811979
%H A302069 R. H. Hardin, <a href="/A302069/b302069.txt">Table of n, a(n) for n = 1..311</a>
%F A302069 Empirical for column k:
%F A302069 k=1: a(n) = 2*a(n-1)
%F A302069 k=2: a(n) = 4*a(n-1)
%F A302069 k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3
%F A302069 k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6
%F A302069 k=5: [order 11] for n>13
%F A302069 k=6: [order 25] for n>27
%F A302069 k=7: [order 53] for n>56
%F A302069 Empirical for row n:
%F A302069 n=1: a(n) = 2*a(n-1)
%F A302069 n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
%F A302069 n=3: [order 15] for n>18
%F A302069 n=4: [order 53] for n>58
%e A302069 Some solutions for n=5 k=4
%e A302069 ..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0
%e A302069 ..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..0..1..0. .0..1..1..1
%e A302069 ..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0
%e A302069 ..1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0. .0..0..1..0
%e A302069 ..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..0..0..1. .0..0..1..0
%Y A302069 Column 1 is A000079(n-1).
%Y A302069 Column 2 is A004171(n-1).
%Y A302069 Row 1 is A000079(n-1).
%Y A302069 Row 2 is A301842.
%K A302069 nonn,tabl
%O A302069 1,2
%A A302069 _R. H. Hardin_, Mar 31 2018