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..500
D. Birmajer, J. B. Gil, M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3 , example 14
Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
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,-3,1)
FORMULA
G.f.: -(3*x^2-5*x+1)/(x^3-3*x^2+5*x-1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-3,5]^n.
MAPLE
a:= n-> (<<0|1|0>, <0|0|1>, <1|-3|5>>^n)[1, 1]:
seq(a(n), n=0..30);
MATHEMATICA
CoefficientList[Series[-(3 x^2 - 5 x + 1)/(x^3 - 3 x^2 + 5 x - 1), {x, 0, 26}], x] (* Michael De Vlieger, Sep 04 2018 *)
LinearRecurrence[{5, -3, 1}, {1, 0, 0}, 40] (* Harvey P. Dale, Aug 18 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Nov 21 2011
STATUS
approved