A392131 - OEIS

A392131

a(n) is the determinant of the n X n circulant matrix whose rows are formed by successively rotating the vector (A000129(0), A000129(1), ..., A000129(n-1)) right.

1, 0, 1, 9, 640, 252100, 597791376, 8252767236301, 665993168101048320, 313398861092499186897912, 859858277306561684298748471552, 13751722491910335588624048111158497953, 1281922118247965546737056182821273600000000000, 696508759202841219994984822691854206568914419368757980

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OFFSET

0,4

COMMENTS

a(n) is the determinant of the n X n Toeplitz matrix whose first column is formed by the vector(A000129(n-1), A000129(n-2), ..., A000129(0)) and whose first row is obtained by rotating once the vector (A000129(0), A000129(1), ..., A000129(n-1)) right.

LINKS

Table of n, a(n) for n=0..13.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Wikipedia, Toeplitz matrix.

FORMULA

Conjecture: lim_{n->oo} A392132(n)/a(n) = 1.

EXAMPLE

a(4) = 640:

[5, 0, 1, 2]

[2, 5, 0, 1]

[1, 2, 5, 0]

[0, 1, 2, 5]

MATHEMATICA

A000129[n_]:=Fibonacci[n, 2]; CirculantMatrix[l_List?VectorQ]:=NestList[RotateRight, RotateRight[l], Length[l] - 1]; a[n_]:=Det[CirculantMatrix[A000129[Range[0, n-1]]]]; Join[{1}, Array[a, 13]] (* or *)

A000129[i_]:=Fibonacci[i, 2]; a[n_]:=Det[ToeplitzMatrix[Reverse[Array[A000129, n, 0]], Join[{A000129[n-1]}, Array[A000129, n-1, 0]]]]; Join[{1}, Array[a, 13]]

CROSSREFS

Cf. A000129, A086459, A118713, A318173, A392132 (permanent).

Sequence in context: A158881 A188394 A157597 * A211611 A280904 A210053

Adjacent sequences: A392128 A392129 A392130 * A392132 A392133 A392134

KEYWORD

nonn

AUTHOR

Stefano Spezia, Dec 31 2025

STATUS

approved