A370724 Determinant of n X n Fibonacci word matrix.

1, 0, -1, 1, -1, 2, 0, 3, 3, 27, 0, 4, 0, 5, 5, 198, 0, 618, 7, 7, 0, 8, 0, 9, 2295, 74349, 0, 18970, -28160, 11, -178717, 12, 0, 57132, -13, 13, -3247328, 14, -1580068, 122895, -94575, 19711504, 0, 111678928, -4001885, 5302759, -4875304727, 18, 0, 194717339, 19

Offset

0,6

Comments

Take the first n terms of A003849 and form an n X n matrix by rotating these n terms 1 place to the left in each new row (i.e., a circulant matrix). This sequence is the determinant of the resulting matrix.

Links

Table of n, a(n) for n=0..50.

Formula

Conjectures: a(F(n)) = +-F(n-2) where F(n) is the n-th Fibonacci number, and a(L(n)) = +-L(n-2) where L(n) is the n-th Lucas number.

Example

For n=5 the first 5 terms are [0,1,0,0,1] and the resulting matrix is [[0,1,0,0,1],[1,0,1,0,0],[0,1,0,1,0],[0,0,1,0,1],[1,0,0,1,0]].  Its determinant is 2.

Crossrefs

Cf. A000032, A000045, A003849, A370725.

Sequence in context: A343980 A021835 A112476 * A321527 A224226 A153250

Adjacent sequences: A370721 A370722 A370723 * A370725 A370726 A370727

Keyword

sign

Author

Jeffrey Shallit, Feb 28 2024

Status

approved