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

56, 672, 13440, 443520, 23950080, 2107607040, 301387806720, 69921971159040, 26290661155799040, 16011012643881615360, 15786858466867272744960, 25195826113120167300956160, 65080818850189392138369761280

Offset: 1

Author

R. H. Hardin, May 12 2011

Keywords

• nonn

Comments

From John M. Campbell, May 25 2011: (Start)

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)

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..60

Programs

Mathematica

Table[Det[Array[KroneckerDelta[#1,#2](Fibonacci[#1+1]-1)+1&,{n,n}]],{n,5,20}]  (* John M. Campbell, May 25 2011 *)

PARI

a(n) = matdet(matrix(n+4, n+4, i, j, if (i==j, fibonacci(i+1), 1))); \\ Michel Marcus, Jan 03 2016