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A302965 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302965 #4 Apr 16 2018 11:55:29
%S A302965 1,2,2,4,8,4,8,29,32,8,16,105,154,128,16,32,384,786,833,512,32,64,
%T A302965 1405,3924,6206,4527,2048,64,128,5135,19868,43588,49521,24602,8192,
%U A302965 128,256,18766,100161,314989,493132,395493,133757,32768,256,512,68589,505908
%N A302965 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302965 Table starts
%C A302965 ...1......2.......4.........8.........16...........32.............64
%C A302965 ...2......8......29.......105........384.........1405...........5135
%C A302965 ...4.....32.....154.......786.......3924........19868.........100161
%C A302965 ...8....128.....833......6206......43588.......314989........2257439
%C A302965 ..16....512....4527.....49521.....493132......5122000.......52646395
%C A302965 ..32...2048...24602....395493....5602382.....83644490.....1233435694
%C A302965 ..64...8192..133757...3157171...63612987...1365216668....28906043997
%C A302965 .128..32768..727293..25208524..722646394..22301032112...677939939546
%C A302965 .256.131072.3954552.201291251.8212135689.364489574945.15913688413086
%H A302965 R. H. Hardin, <a href="/A302965/b302965.txt">Table of n, a(n) for n = 1..180</a>
%F A302965 Empirical for column k:
%F A302965 k=1: a(n) = 2*a(n-1)
%F A302965 k=2: a(n) = 4*a(n-1)
%F A302965 k=3: a(n) = 7*a(n-1) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6
%F A302965 k=4: [order 19] for n>20
%F A302965 k=5: [order 80] for n>81
%F A302965 Empirical for row n:
%F A302965 n=1: a(n) = 2*a(n-1)
%F A302965 n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F A302965 n=3: [order 12] for n>13
%F A302965 n=4: [order 44] for n>45
%e A302965 Some solutions for n=5 k=4
%e A302965 ..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..1..0. .0..0..1..0
%e A302965 ..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..0..1..1. .1..0..1..0
%e A302965 ..0..1..0..0. .1..1..1..1. .1..0..1..1. .0..1..0..0. .1..0..1..0
%e A302965 ..1..1..1..1. .1..0..0..1. .1..0..1..0. .0..1..0..0. .1..0..1..1
%e A302965 ..1..0..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..0..0
%Y A302965 Column 1 is A000079(n-1).
%Y A302965 Column 2 is A004171(n-1).
%Y A302965 Row 1 is A000079(n-1).
%Y A302965 Row 2 is A302266.
%K A302965 nonn,tabl
%O A302965 1,2
%A A302965 _R. H. Hardin_, Apr 16 2018