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A146083 Expansion of 1/(1 - x*(1 - 11*x)). 4
1, 1, -10, -21, 89, 320, -659, -4179, 3070, 49039, 15269, -524160, -692119, 5073641, 12686950, -43123101, -182679551, 291674560, 2301149621, -907270539, -26219916370, -16239940441, 272179139629, 450818484480, -2543152051439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of Riordan array (1,x(1-11x)).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,-11)

FORMULA

a(n) = a(n-1)-11*a(n-2) ; a(0)=1, a(1)=1.

a(n) = Sum_{k, 0<=k<=n} A109466(n,k)*11^(n-k).

a(n) = (1/2)*[(1/2)+(1/2)*I*sqrt(43)]^n-(1/86)*I*[(1/2)+(1/2)*I*sqrt(43)]^n*sqrt(43)+(1/2)*[(1/2) -(1/2)*I*sqrt(43)]^n+(1/86)*I*[(1/2)-(1/2)*I*sqrt(43)]^n*sqrt(43), with n>=0 and I=sqrt(-1). - Paolo P. Lava, Nov 18 2008

From G. C. Greubel, Jan 31 2016 (Start)

G.f.: 1/(1-x+11*x^2).

E.g.f.: exp(x/2)*(cos(sqrt(43)*x/2) + (1/sqrt(43))*sin(sqrt(43)*x/2)).

(End)

MATHEMATICA

Join[{a=1, b=1}, Table[c=b-11*a; a=b; b=c, {n, 80}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)

LinearRecurrence[{1, -11}, {1, 1}, 30] (* Harvey P. Dale, Jan 07 2016 *)

PROG

(Sage) [lucas_number1(n, 1, 11) for n in xrange(1, 26)] # Zerinvary Lajos, Apr 22 2009

(PARI) Vec(1/(1-x(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

(MAGMA) [n le 2 select 1 else Self(n-1)-11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 31 2016

CROSSREFS

Cf. A010892, A107920, A106852, A106853, A106854, A145934, A145976, A145978, A146078, A146080.

Sequence in context: A041196 A082669 A215574 * A001739 A072805 A119033

Adjacent sequences:  A146080 A146081 A146082 * A146084 A146085 A146086

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 27 2008

STATUS

approved

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Last modified February 21 06:25 EST 2018. Contains 299390 sequences. (Running on oeis4.)