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A283857 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors. 13

%I

%S 2,4,4,8,16,8,16,61,64,16,32,233,409,256,32,64,896,2776,2837,1024,64,

%T 128,3444,19220,35373,19776,4096,128,256,13225,131617,456316,448490,

%U 137459,16384,256,512,50789,901397,5742620,10741381,5676420,955680,65536,512

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.

%C Table starts

%C ...2.....4.......8........16...........32.............64..............128

%C ...4....16......61.......233..........896...........3444............13225

%C ...8....64.....409......2776........19220.........131617...........901397

%C ..16...256....2837.....35373.......456316........5742620.........72394838

%C ..32..1024...19776....448490.....10741381......247708452.......5724272337

%C ..64..4096..137459...5676420....252014450....10634931992.....449942735521

%C .128.16384..955680..71903903...5921518755...457711375590...35481195059121

%C .256.65536.6645662.910712188.139111379622.19691576356912.2796411775700471

%H R. H. Hardin, <a href="/A283857/b283857.txt">Table of n, a(n) for n = 1..221</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1)

%F k=3: [order 8]

%F k=4: [order 17]

%F k=5: [order 45]

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1)

%F n=2: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4)

%F n=3: [order 14]

%F n=4: [order 28]

%F n=5: [order 74]

%e Some solutions for n=4 k=4

%e ..1..0..0..1. .0..0..1..0. .1..1..1..1. .0..0..0..0. .1..0..1..1

%e ..0..1..1..0. .1..0..0..0. .0..1..0..0. .0..0..0..1. .1..0..1..1

%e ..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..1

%e ..1..1..0..0. .1..0..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1

%Y Column 1 is A000079.

%Y Column 2 is A000302.

%Y Row 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 17 2017

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Last modified January 21 12:51 EST 2022. Contains 350477 sequences. (Running on oeis4.)