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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 Colin Barker, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (82,1). 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:=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 Adjacent sequences: A292420 A292421 A292422 * A292424 A292425 A292426 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.)