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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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.

|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

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 3x3 matrix [0,1,0; 0,0,1; 1,-3,1]^n.

a(0)=1, a(1)=a(2)=0, a(n)=a(n-1)-3*a(n-2)+a(n-3). - 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

Cf. A200676, A200739.

Sequence in context: A181327 A257503 A091861 * A079308 A189825 A271878

Adjacent sequences:  A200712 A200713 A200714 * A200716 A200717 A200718

KEYWORD

sign,easy

AUTHOR

Alois P. Heinz, Nov 21 2011

STATUS

approved

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Last modified November 19 01:27 EST 2017. Contains 294912 sequences.