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A014992 a(n) = (1 - (-10)^n)/11. 9
1, -9, 91, -909, 9091, -90909, 909091, -9090909, 90909091, -909090909, 9090909091, -90909090909, 909090909091, -9090909090909, 90909090909091, -909090909090909, 9090909090909091, -90909090909090909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

q-integers for q = -10.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (-9,10).

FORMULA

a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).

G.f.: x/((1 - x)*(1 + 10*x)). - Vincenzo Librandi, Oct 22 2012

a(n) = -9*a(n-1) + 10*a(n-2). - Vincenzo Librandi, Oct 22 2012

a(n) = (-1)^(n+1)*A015585(n). - R. J. Mathar, Oct 26 2015

MAPLE

a:=n->sum ((-10)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008

MATHEMATICA

CoefficientList[Series[1/((1 - x)*(1 + 10*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2012 *)

PROG

(Sage) [gaussian_binomial(n, 1, -10) for n in xrange(1, 19)] # Zerinvary Lajos, May 28 2009

(MAGMA) I:=[1, -9]; [n le 2 select I[n] else -9*Self(n-1) +10*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

CROSSREFS

A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014993, A014994. - Zerinvary Lajos, Dec 16 2008

Sequence in context: A020243 A239867 A217959 * A015585 A242299 A109108

Adjacent sequences:  A014989 A014990 A014991 * A014993 A014994 A014995

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Better name from Ralf Stephan, Jul 14 2013

STATUS

approved

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Last modified February 21 19:26 EST 2018. Contains 299422 sequences. (Running on oeis4.)