OFFSET
0,6
COMMENTS
Peter Lawrence (see links) has posted a challenge to find a 3 X 3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found.
|a(n)| is a prime number for n in {5, 7, 8, 11, 19, 27, 108, 276, 371, 608, ...} with values {2, 3, 13, 23, 3359, 69481, 167527749243856707416101, ...}.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
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 (1,-3,1)
FORMULA
G.f.: (-3*x^2 + x - 1)/(x^3 - 3*x^2 + x - 1).
Term (1,1) in the 3 X 3 matrix [0,1,0; 0,0,1; 1,-3,1]^n.
a(n) = a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=a(2)=0. - Harvey P. Dale, Nov 22 2011
MAPLE
a:= n-> (<<0|1|0>, <0|0|1>, <1|-3|1>>^n)[1, 1]:
seq(a(n), n=0..50);
MATHEMATICA
CoefficientList[Series[(-3x^2+x-1)/(x^3-3x^2+x-1), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, -3, 1}, {1, 0, 0}, 40] (* Harvey P. Dale, Nov 22 2011 *)
PROG
(PARI) Vec((-3*x^2+x-1)/(x^3-3*x^2+x-1)+O(x^99)) \\ Charles R Greathouse IV, Nov 22 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Alois P. Heinz, Nov 21 2011
STATUS
approved