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Number of n X 6 binary arrays without the pattern 0 1 diagonally or antidiagonally.
1

%I #8 Apr 30 2018 08:56:18

%S 64,441,1296,2704,4624,7056,10000,13456,17424,21904,26896,32400,38416,

%T 44944,51984,59536,67600,76176,85264,94864,104976,115600,126736,

%U 138384,150544,163216,176400,190096,204304,219024,234256,250000,266256,283024

%N Number of n X 6 binary arrays without the pattern 0 1 diagonally or antidiagonally.

%C Column 6 of A188824.

%H R. H. Hardin, <a href="/A188821/b188821.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 256*n^2 - 384*n + 144 for n>2.

%F Conjectures from _Colin Barker_, Apr 30 2018: (Start)

%F G.f.: x*(64 + 249*x + 165*x^2 + 75*x^3 - 41*x^4) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

%F (End)

%e Some solutions for 3 X 6:

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

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

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

%Y Cf. A188824.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 11 2011