OFFSET
0,2
REFERENCES
Alston S. Householder, The Theory of Matrices in Numerical Analysis, Dover, New York, 1964, page 95
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
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 15 2010
STATUS
approved