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A146078 Expansion of 1/(1-x*(1-9*x)). 6
1, 1, -8, -17, 55, 208, -287, -2159, 424, 19855, 16039, -162656, -307007, 1156897, 3919960, -6492113, -41771753, 16657264, 392603041, 242687665, -3290739704, -5474928689, 24141728647, 73416086848, -143859470975, -804604252607 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of Riordan array (1, x(1-9x)).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,-9).

FORMULA

a(n) = a(n-1) - 9*a(n-2), a(0)=1, a(1)=1.

a(n) = Sum_{k=0..n} A109466(n,k)*9^(n-k).

a(n) = -(1/70)*i*sqrt(35)*(1/2 + (1/2)*i*sqrt(35))^n + (1/70)*i*sqrt(35)*(1/2 - (1/2)*i*sqrt(35))^n + (1/2)*(1/2 + (1/2)*i*sqrt(35))^n + (1/2)*(1/2 - (1/2)*i*sqrt(35))^n for n >= 0, where i=sqrt(-1). - Paolo P. Lava, Nov 18 2008

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

G.f.: 1/(1-x+9*x^2).

E.g.f.: exp(x/2)*(cos(sqrt(35)*x/2) + (1/sqrt(35))*sin(sqrt(35)*x/2)). (End)

a(n) = Product_{k=1..n}(1 + 6*cos(k*Pi/(n+1)). - Peter Luschny, Nov 28 2019

MAPLE

a:=series(1/(1-x*(1-9*x)), x=0, 26):

seq(coeff(a, x, n), n=0..25); # Paolo P. Lava, Mar 28 2019

MATHEMATICA

LinearRecurrence[{1, -9}, {1, 1}, 100] (* G. C. Greubel, Jan 30 2016 *)

PROG

(Sage) [lucas_number1(n, 1, 9) for n in range(1, 27)] # Zerinvary Lajos, Apr 22 2009

(PARI) x='x+O('x^30); Vec(1/(1-x+9*x^2)) \\ G. C. Greubel, Jan 19 2018

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else Self(n-1) - 9*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 19 2018

CROSSREFS

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

Sequence in context: A111325 A173056 A008782 * A097058 A186255 A244792

Adjacent sequences:  A146075 A146076 A146077 * A146079 A146080 A146081

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 27 2008

STATUS

approved

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Last modified December 7 02:57 EST 2021. Contains 349567 sequences. (Running on oeis4.)