A019447 Number of monomials in expansion of determinant of an n X n Toeplitz matrix [ t(|i-j|) ] in terms of its entries.

1, 1, 2, 4, 12, 35, 120, 427, 1628, 6090, 23797, 90296, 350726, 1338076, 5165957, 19732508

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Maple

with(LinearAlgebra): f:=n->nops([coeffs(Determinant(Matrix(n, (i, j) -> a[abs(i-j)])))]): [seq(f(n), n=0..12)];

Mathematica

f[n_] := Length[ Expand[ Det[ Table[ t[ Abs[ i - j]], {i, 1, n}, {j, 1, n}]]]]; Table[ f[n], {n, 1, 11}]

Crossrefs

Cf. A019448, A086647.

Sequence in context: A148204 A151525 A148205 * A148206 A148207 A331621

Adjacent sequences: A019444 A019445 A019446 * A019448 A019449 A019450

Keyword

nonn,more,hard

Author

Herbert S. Wilf

Extensions

Terms a(12) and a(13) from Thotsaporn Thanatipanonda, Jan 26-28 2012

Terms a(14) and a(15) from Roman Pearce, Aug 30 2014

a(0)=1 prepended by Alois P. Heinz, Feb 25 2024

Status

approved