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A292423 a(n) = 82*a(n-1) + a(n-2), where a(0) = 0, a(1) = 1. 1
0, 1, 82, 6725, 551532, 45232349, 3709604150, 304232772649, 24950796961368, 2046269583604825, 167819056652557018, 13763208915093280301, 1128750950094301541700, 92571341116647819699701, 7591978722515215516917182, 622634826587364320206908625 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Every fifth term of A000129 is divisible by 29. Dividing every fifth term by 29 gives this sequence.
LINKS
FORMULA
a(n) = A000129(5*n)/29.
From Colin Barker, Sep 20 2017: (Start)
G.f.: x / (1 - 82*x - x^2).
a(n) = (((-41-29*sqrt(2))^(-n)*(-1 + (-3363-2378*sqrt(2))^n))) / (58*sqrt(2)).
(End)
MAPLE
a:= n-> (<<0|1>, <1|82>>^n)[1, 2]:
seq(a(n), n=0..20); # Alois P. Heinz, Sep 18 2017
MATHEMATICA
CoefficientList[Series[x/(1-82*x-x^2), {x, 0, 20}], x] (* G. C. Greubel, Feb 02 2019 *)
PROG
(PARI) a(n) = ([82, 1; 1, 0]^n)[2, 1]; \\ Altug Alkan, Sep 18 2017
(PARI) concat(0, Vec(x / (1 - 82*x - x^2) + O(x^20))) \\ Colin Barker, Sep 20 2017
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x/(1-82*x-x^2) )); // G. C. Greubel, Feb 02 2019
(Sage) (x/(1-82*x-x^2)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Feb 02 2019
CROSSREFS
Cf. A000129.
Sequence in context: A280959 A252705 A239670 * A097841 A116123 A116142
KEYWORD
nonn,easy
AUTHOR
Bobby Jacobs, Sep 18 2017
STATUS
approved

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Last modified April 19 12:14 EDT 2024. Contains 371792 sequences. (Running on oeis4.)