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A190535
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Number of (n+2) X (n+2) symmetric binary matrices without the pattern 0 1 1 diagonally.
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2
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56, 672, 13440, 443520, 23950080, 2107607040, 301387806720, 69921971159040, 26290661155799040, 16011012643881615360, 15786858466867272744960, 25195826113120167300956160, 65080818850189392138369761280
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OFFSET
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1,1
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COMMENTS
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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
{{1,1,1,1,1,1},
{1,2,1,1,1,1},
{1,1,3,1,1,1},
{1,1,1,5,1,1},
{1,1,1,1,8,1},
{1,1,1,1,1,13}}. (End)
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LINKS
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EXAMPLE
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Some solutions for 4 X 4:
..0..1..0..1....1..1..1..1....0..1..1..0....0..1..1..1....1..1..1..1
..1..0..0..0....1..0..0..0....1..1..1..0....1..1..0..1....1..0..0..1
..0..0..0..0....1..0..0..0....1..1..0..1....1..0..0..1....1..0..0..0
..1..0..0..0....1..0..0..1....0..0..1..1....1..1..1..0....1..1..0..0
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MATHEMATICA
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Table[Det[Array[KroneckerDelta[#1, #2](Fibonacci[#1+1]-1)+1&, {n, n}]], {n, 5, 20}] (* John M. Campbell, May 25 2011 *)
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PROG
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(PARI) a(n) = matdet(matrix(n+4, n+4, i, j, if (i==j, fibonacci(i+1), 1))); \\ Michel Marcus, Jan 03 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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