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A141527 Expansion of x*(x+2) / (41*x^2+x+1). 0
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

Table of n, a(n) for n=1..22.

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

FORMULA

c0 = (-1-sqrt(163)*i)/2; c1=(-1+sqrt(163)*i)/2; a(n) = c0^n + c1^n.

a(n) = -a(n-1) -41*a(n-2). G.f.: x*(x+2) / (41*x^2+x+1). - Colin Barker, Mar 17 2013

a(n) = -a(n-1) -41*a(n-2). - Colin Barker, Mar 17 2013

MATHEMATICA

a = x /. Solve[x^2 + x + 41 == 0, x][[1]]; b = x /. Solve[x^2 + x + 41 == 0, x][[2]]; f[n_] = (a^n + b^n); Table[ExpandAll[f[n]], {n, 0, 50}]

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

CROSSREFS

Cf. A005846.

Sequence in context: A095837 A095835 A147805 * A191298 A104025 A039923

Adjacent sequences:  A141524 A141525 A141526 * A141528 A141529 A141530

KEYWORD

sign,easy

AUTHOR

Roger L. Bagula, Aug 11 2008

EXTENSIONS

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

STATUS

approved

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.