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Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
2

%I #13 Mar 30 2017 16:23:17

%S 1,2,7,26,95,340,1193,4116,14001,47064,156629,516844,1693073,5511218,

%T 17841247,57477542,184377699,589195584,1876395357,5957318820,

%U 18861068265,59563612974,187668462027,590039959434,1851508693479,5799494052414,18135645594003

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

%C Diagonal of A188866.

%H Alois P. Heinz, <a href="/A188860/b188860.txt">Table of n, a(n) for n = 0..2000</a> (terms n = 1..32 from R. H. Hardin)

%F G.f.: (3*x^2-3*x+1-x*sqrt(1-3*x^2-2*x))/(1-3*x)^2. - _Alois P. Heinz_, Mar 30 2017

%e Some solutions for 3X3

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

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

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

%p a:= proc(n) option remember; `if`(n<3, (2*n-1)*n+1,

%p ((10*n^2-49*n+33)*a(n-1)-(6*n^2-9*n-33)*a(n-2)

%p -(9*(n-3))*(2*n-7)*a(n-3))/((n-1)*(2*n-9)))

%p end:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Mar 30 2017

%Y Cf. A188866.

%K nonn

%O 0,2

%A _R. H. Hardin_, Apr 12 2011

%E a(0)=1 prepended by _Alois P. Heinz_, Mar 30 2017