cp's OEIS Frontend

A188860 Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

%I A188860 #13 Mar 30 2017 16:23:17
%S A188860 1,2,7,26,95,340,1193,4116,14001,47064,156629,516844,1693073,5511218,
%T A188860 17841247,57477542,184377699,589195584,1876395357,5957318820,
%U A188860 18861068265,59563612974,187668462027,590039959434,1851508693479,5799494052414,18135645594003
%N A188860 Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
%C A188860 Diagonal of A188866.
%H A188860 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 A188860 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 A188860 Some solutions for 3X3
%e A188860 ..1..1..1....0..0..0....1..1..1....1..1..1....1..1..0....1..1..1....1..1..1
%e A188860 ..1..1..1....0..0..0....1..1..1....1..0..0....0..0..0....1..1..1....1..1..1
%e A188860 ..1..1..0....0..0..0....1..0..0....0..0..0....0..0..0....1..0..1....0..0..0
%p A188860 a:= proc(n) option remember; `if`(n<3, (2*n-1)*n+1,
%p A188860       ((10*n^2-49*n+33)*a(n-1)-(6*n^2-9*n-33)*a(n-2)
%p A188860        -(9*(n-3))*(2*n-7)*a(n-3))/((n-1)*(2*n-9)))
%p A188860     end:
%p A188860 seq(a(n), n=0..35);  # _Alois P. Heinz_, Mar 30 2017
%Y A188860 Cf. A188866.
%K A188860 nonn
%O A188860 0,2
%A A188860 _R. H. Hardin_, Apr 12 2011
%E A188860 a(0)=1 prepended by _Alois P. Heinz_, Mar 30 2017