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A302265 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302265 #4 Apr 04 2018 12:50:47
%S A302265 1,2,2,4,8,4,8,29,32,8,16,105,153,128,16,32,384,772,818,512,32,64,
%T A302265 1405,3818,5922,4386,2048,64,128,5135,19191,40296,45717,23516,8192,
%U A302265 128,256,18766,96004,284428,429854,353229,126162,32768,256,512,68589,481261
%N A302265 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302265 Table starts
%C A302265 ...1......2.......4.........8.........16...........32............64
%C A302265 ...2......8......29.......105........384.........1405..........5135
%C A302265 ...4.....32.....153.......772.......3818........19191.........96004
%C A302265 ...8....128.....818......5922......40296.......284428.......1984001
%C A302265 ..16....512....4386.....45717.....429854......4289139......41994750
%C A302265 ..32...2048...23516....353229....4608075.....64975832.....893462062
%C A302265 ..64...8192..126162...2727755...49315068....982041385...18964765818
%C A302265 .128..32768..676988..21069318..527911860..14850510984..402597400706
%C A302265 .256.131072.3632880.162753849.5651844495.224584502616.8547940665506
%H A302265 R. H. Hardin, <a href="/A302265/b302265.txt">Table of n, a(n) for n = 1..180</a>
%F A302265 Empirical for column k:
%F A302265 k=1: a(n) = 2*a(n-1)
%F A302265 k=2: a(n) = 4*a(n-1)
%F A302265 k=3: a(n) = 6*a(n-1) -2*a(n-2) +2*a(n-3) -54*a(n-4) +16*a(n-5) for n>6
%F A302265 k=4: [order 17] for n>18
%F A302265 k=5: [order 70] for n>71
%F A302265 Empirical for row n:
%F A302265 n=1: a(n) = 2*a(n-1)
%F A302265 n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F A302265 n=3: [order 12] for n>13
%F A302265 n=4: [order 44] for n>45
%e A302265 Some solutions for n=5 k=4
%e A302265 ..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..1..0
%e A302265 ..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..0. .1..0..1..1
%e A302265 ..1..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..1. .1..1..0..0
%e A302265 ..0..1..1..1. .1..1..0..1. .0..1..0..0. .0..1..0..1. .0..1..0..1
%e A302265 ..1..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..1..0. .1..1..0..0
%Y A302265 Column 1 is A000079(n-1).
%Y A302265 Column 2 is A004171(n-1).
%Y A302265 Row 1 is A000079(n-1).
%K A302265 nonn,tabl
%O A302265 1,2
%A A302265 _R. H. Hardin_, Apr 04 2018