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 A190535 Number of (n+2) X (n+2) symmetric binary matrices without the pattern 0 1 1 diagonally. 2

%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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Last modified April 18 13:10 EDT 2024. Contains 371780 sequences. (Running on oeis4.)