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A200676 Expansion of -(3*x^2-5*x+1)/(x^3-3*x^2+5*x-1). 4
1, 0, 0, 1, 5, 22, 96, 419, 1829, 7984, 34852, 152137, 664113, 2899006, 12654828, 55241235, 241140697, 1052634608, 4594992184, 20058197793, 87558647021, 382213633910, 1668450426280, 7283169876691, 31792711738525, 138782499488832, 605817532105276 (list; graph; refs; listen; history; text; internal format)
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

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);

CROSSREFS

Cf. A200739.

Sequence in context: A026888 A266430 A083586 * A129158 A129164 A123347

Adjacent sequences:  A200673 A200674 A200675 * A200677 A200678 A200679

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Nov 21 2011

STATUS

approved

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Last modified May 28 16:19 EDT 2017. Contains 287241 sequences.