

A200676


Expansion of (3*x^25*x+1)/(x^33*x^2+5*x1).


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
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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..500
D. Birmajer, J. B. Gil, M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3 , example 14
Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
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 (5,3,1)


FORMULA

G.f.: (3*x^25*x+1)/(x^33*x^2+5*x1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,3,5]^n.


MAPLE

a:= n> (<<010>, <001>, <135>>^n)[1, 1]:
seq(a(n), n=0..30);


MATHEMATICA

CoefficientList[Series[(3 x^2  5 x + 1)/(x^3  3 x^2 + 5 x  1), {x, 0, 26}], x] (* Michael De Vlieger, Sep 04 2018 *)
LinearRecurrence[{5, 3, 1}, {1, 0, 0}, 40] (* Harvey P. Dale, Aug 18 2021 *)


CROSSREFS

Cf. A200739.
Sequence in context: A026888 A266430 A083586 * A297333 A129158 A342554
Adjacent sequences: A200673 A200674 A200675 * A200677 A200678 A200679


KEYWORD

nonn,easy


AUTHOR

Alois P. Heinz, Nov 21 2011


STATUS

approved



