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%I #16 Jan 03 2016 03:53:48
%S 56,672,13440,443520,23950080,2107607040,301387806720,69921971159040,
%T 26290661155799040,16011012643881615360,15786858466867272744960,
%U 25195826113120167300956160,65080818850189392138369761280
%N Number of (n+2) X (n+2) symmetric binary matrices without the pattern 0 1 1 diagonally.
%C From _John M. Campbell_, May 25 2011: (Start)
%C a(n) equals the determinant of the (n+4) X (n+4) "Fibonacci matrix" whose (i,j)-entry is equal to F_{i+1} if i=j and is equal to 1 otherwise. For example, a(2)=672 equals the determinant of the 6 X 6 Fibonacci matrix
%C {{1,1,1,1,1,1},
%C {1,2,1,1,1,1},
%C {1,1,3,1,1,1},
%C {1,1,1,5,1,1},
%C {1,1,1,1,8,1},
%C {1,1,1,1,1,13}}. (End)
%H R. H. Hardin, <a href="/A190535/b190535.txt">Table of n, a(n) for n = 1..60</a>
%e Some solutions for 4 X 4:
%e ..0..1..0..1....1..1..1..1....0..1..1..0....0..1..1..1....1..1..1..1
%e ..1..0..0..0....1..0..0..0....1..1..1..0....1..1..0..1....1..0..0..1
%e ..0..0..0..0....1..0..0..0....1..1..0..1....1..0..0..1....1..0..0..0
%e ..1..0..0..0....1..0..0..1....0..0..1..1....1..1..1..0....1..1..0..0
%t Table[Det[Array[KroneckerDelta[#1,#2](Fibonacci[#1+1]-1)+1&,{n,n}]],{n,5,20}] (* _John M. Campbell_, May 25 2011 *)
%o (PARI) a(n) = matdet(matrix(n+4, n+4, i, j, if (i==j, fibonacci(i+1), 1))); \\ _Michel Marcus_, Jan 03 2016
%K nonn
%O 1,1
%A _R. H. Hardin_, May 12 2011
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