OFFSET
1,2
COMMENTS
REFERENCES
Carl D. Meyer, "Matrix Analysis and Applied Linear Algebra", SIAM, 2000, pp. 86.-87.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8,-9).
FORMULA
a(n) = (3/(2*sqrt(7)))*((4+sqrt(7))^(n-1)-(4-sqrt(7))^(n-1)). For n>1, a(n) = 3*A154245(n-1). - Francesco Daddi, Aug 02 2011
G.f.: 3*x^2/(1-8*x+9*x^2). - Bruno Berselli, Aug 03 2011
EXAMPLE
a(4) = 165 since M^4 * [1 0 0] = [38 -203 165].
MATHEMATICA
Table[(MatrixPower[{{1, -1, 0}, {-1, 4, -3}, {0, -3, 3}}, n].{1, 0, 0})[[3]], {n, 21}] (* Robert G. Wilson v, May 08 2004 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 02 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 08 2004
STATUS
approved