A292423 a(n) = 82*a(n-1) + a(n-2), where a(0) = 0, a(1) = 1.

0, 1, 82, 6725, 551532, 45232349, 3709604150, 304232772649, 24950796961368, 2046269583604825, 167819056652557018, 13763208915093280301, 1128750950094301541700, 92571341116647819699701, 7591978722515215516917182, 622634826587364320206908625

Offset: 0

Author

Bobby Jacobs, Sep 18 2017

Keywords

• nonn
• easy

Comments

Every fifth term of A000129 is divisible by 29. Dividing every fifth term by 29 gives this sequence.

Links

• Colin Barker, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (82,1).

Crossrefs

Cf. A000129.

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x/(1-82*x-x^2) )); // G. C. Greubel, Feb 02 2019

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 *)
LinearRecurrence[{82,1},{0,1},20] (* Harvey P. Dale, Dec 20 2024 *)

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

Sage

(x/(1-82*x-x^2)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Feb 02 2019

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)