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A146080 Expansion of 1/(1-x*(1-10*x)). 6
1, 1, -9, -19, 71, 261, -449, -3059, 1431, 32021, 17711, -302499, -479609, 2545381, 7341471, -18112339, -91527049, 89596341, 1004866831, 108903421, -9939764889, -11028799099, 88368849791, 198656840781, -685031657129, -2671600064939 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of Riordan array (1,x(1-10x)).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,-10).

FORMULA

a(n) = a(n-1) - 10*a(n-2), a(0)=1, a(1)=1.

a(n) = Sum_{k=0..n} A109466(n,k)*10^(n-k).

a(n) = -(1/78)*i*(1/2 + (1/2)*i*sqrt(39))^n*sqrt(39) + (1/2)*(1/2 + (1/2)*i*sqrt(39))^n + (1/78)*i*sqrt(39)*(1/2 - (1/2)*i*sqrt(39))^n + (1/2)*(1/2 - (1/2)*i*sqrt(39))^n, with n>=0 and i=sqrt(-1). - Paolo P. Lava, Nov 18 2008

E.g.f.: exp(x/2)*(cos(sqrt(39)*x/2) + (1/sqrt(39))*sin(sqrt(39)*x/2)). - G. C. Greubel, Jan 30 2016

MATHEMATICA

Join[{a=1, b=1}, Table[c=b-10*a; a=b; b=c, {n, 80}]]

(* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)

CoefficientList[Series[1/(1-x(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, -10}, {1, 1}, 30] (* Harvey P. Dale, Dec 16 2012 *)

PROG

(Sage) [lucas_number1(n, 1, 10) for n in xrange(1, 27)] # Zerinvary Lajos, Apr 22 2009

(PARI) Vec(1/(1-x*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 10*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 19 2018

CROSSREFS

Sequence in context: A046103 A146459 A041158 * A259093 A186508 A000981

Adjacent sequences:  A146077 A146078 A146079 * A146081 A146082 A146083

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 27 2008

STATUS

approved

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Last modified October 23 05:50 EDT 2018. Contains 316519 sequences. (Running on oeis4.)