OFFSET
0,5
COMMENTS
Peter Lawrence (see links) has posted a challenge to find a 3x3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
Peter Lawrence et al., sequence challenge and follow-up messages on the SeqFan list, Nov 21 2011
Index entries for linear recurrences with constant coefficients, signature (5,-1,1)
FORMULA
G.f.: (-x^2+5*x-1)/(x^3-x^2+5*x-1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-1,5]^n.
MAPLE
a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|5>>^n)[1, 1]:
seq(a(n), n=0..30);
MATHEMATICA
CoefficientList[Series[(-x^2 + 5 x - 1)/(x^3 - x^2 + 5 x - 1), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, -1, 1}, {1, 0, 0}, 30] (* Harvey P. Dale, Nov 26 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 21 2011
STATUS
approved