

A200739


Expansion of (x^2+5*x1)/(x^3x^2+5*x1).


4



1, 0, 0, 1, 5, 24, 116, 561, 2713, 13120, 63448, 306833, 1483837, 7175800, 34701996, 167818017, 811563889, 3924703424, 18979771248, 91785716705, 443873515701, 2146561633048, 10380720366244, 50200913713873, 242770409836169, 1174031855833216, 5677589783043784
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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..450
Peter Lawrence et al., sequence challenge and followup messages on the SeqFan list, Nov 21 2011
Index entries for linear recurrences with constant coefficients, signature (5,1,1)


FORMULA

G.f.: (x^2+5*x1)/(x^3x^2+5*x1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,1,5]^n.


MAPLE

a:= n> (<<010>, <001>, <115>>^n)[1, 1]:
seq(a(n), n=0..30);


MATHEMATICA

CoefficientList[Series[(x^2 + 5 x  1)/(x^3  x^2 + 5 x  1), {x, 0, 30}], x] (* or *) LinearRecurrence[{5, 1, 1}, {1, 0, 0}, 30] (* Harvey P. Dale, Nov 26 2017 *)


CROSSREFS

Cf. A200676.
Sequence in context: A057969 A004254 A086347 * A026707 A235115 A110190
Adjacent sequences: A200736 A200737 A200738 * A200740 A200741 A200742


KEYWORD

nonn,easy


AUTHOR

Alois P. Heinz, Nov 21 2011


STATUS

approved



