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A200715
Expansion of (-3*x^2 + x - 1)/(x^3 - 3*x^2 + x - 1).
2
1, 0, 0, 1, 1, -2, -4, 3, 13, 0, -36, -23, 85, 118, -160, -429, 169, 1296, 360, -3359, -3143, 7294, 13364, -11661, -44459, 3888, 125604, 69481, -303443, -386282, 593528, 1448931, -717935, -4471200, -868464, 11827201, 9961393, -26388674, -44445652, 44681763
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
Peter Lawrence et al., sequence challenge and follow-up messages on the SeqFan list, Nov 21 2011
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
Sequence in context: A181327 A257503 A091861 * A297901 A079308 A189825
KEYWORD
sign,easy
AUTHOR
Alois P. Heinz, Nov 21 2011
STATUS
approved