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A141527 Expansion of x*(2 + x)/(1 + x + 41*x^2). 2
2, -1, -81, 122, 3199, -8201, -122958, 459199, 4582079, -23409238, -164456001, 1124234759, 5618461282, -51712086401, -178644826161, 2298840368602, 5025597503999, -99278052616681, -106771445047278, 4177171602331199, 200457644607199, -171464493340186358 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (-1,-41).

FORMULA

a(n) = (-1)^n*(p^n + q^n), where p = (1 +sqrt(163)*i)/2 and q = (1 -sqrt(163)*i)/2.

From Colin Barker, Mar 17 2013: (Start)

a(n) = -a(n-1) -41*a(n-2), with a(0) = 2 and a(1) = -1.

G.f.: x*(2+x)/(1 +x +41*x^2). (End)

MATHEMATICA

(* First program *)

p:= (1 +Sqrt[163]*I)/2; q:= (1 -Sqrt[163]*I)/2; f[n_]:= (-1)^n*(p^n + q^n); Table[Simplify[f[n]], {n, 0, 30}] (* modified by G. C. Greubel, Mar 29 2021 *)

(* Second program *)

LinearRecurrence[{-1, -41}, {2, -1}, 30] (* Harvey P. Dale, Sep 04 2015 *)

PROG

(Magma)

R<x>:=PowerSeriesRing(Rationals(), 30);

Coefficients(R!( x*(2+x)/(1+x+41*x^2) )); // G. C. Greubel, Mar 29 2021

(Sage)

def A141527_list(prec):

    P.<x> = PowerSeriesRing(QQ, prec)

    return P( x*(2+x)/(1+x+41*x^2) ).list()

a=A141527_list(31); a[1:] # G. C. Greubel, Mar 29 2021

CROSSREFS

Cf. A005846, A141528.

Sequence in context: A095837 A095835 A147805 * A301631 A191298 A104025

Adjacent sequences:  A141524 A141525 A141526 * A141528 A141529 A141530

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Aug 11 2008

EXTENSIONS

New name from Colin Barker and Joerg Arndt, Mar 17 2013

STATUS

approved

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Last modified September 27 09:22 EDT 2022. Contains 357054 sequences. (Running on oeis4.)