A174320 A determinant sequence of a matrix recursion: x(n)=x(n-1).(2*I-A.x(n-1))

1, 5, 85, 8245, 65440565, 4283494440865205, 18348324030778500099729491426485, 336660994738443647199194470007929817797632634753799749499557045, 113340625378278381103431272633178867729689711019442136566960907286489475340193

Offset

0,2

References

Alston S. Householder, The Theory of Matrices in Numerical Analysis, Dover, New York, 1964, page 95

Links

Table of n, a(n) for n=0..8.

Formula

I=x(0);A={{0, 1, 0}, {0, 0, 1}, {1, 1, 0}};

x(n)=x(n-1).(2*I-A.x(n-1))

Limit_{n->infinity} a(n)^(1/2^n) = (388 + 12*sqrt(69))^(1/3)/6 + 26/(3*(388 + 12*sqrt(69))^(1/3)) + 2/3 = 3.079595623491438786010417750836626032629... - Vaclav Kotesovec, Oct 28 2021

Mathematica

Clear[x, A, n]
x[0] := {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
A := {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}};
x[n_] := x[n] = x[n - 1].(2*x[0] - A.x[n - 1]);
Table[Det[x[n]], {n, 0, 10}]

Crossrefs

Sequence in context: A018925 A309327 A363424 * A140159 A073862 A222983

Adjacent sequences: A174317 A174318 A174319 * A174321 A174322 A174323

Keyword

nonn

Author

Roger L. Bagula, Mar 15 2010

Status

approved