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A014993 a(n) = (1 - (-11)^n)/12. 8
1, -10, 111, -1220, 13421, -147630, 1623931, -17863240, 196495641, -2161452050, 23775972551, -261535698060, 2876892678661, -31645819465270, 348104014117971, -3829144155297680, 42120585708274481 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

q-integers for q = -11.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..900

Index entries for linear recurrences with constant coefficients, signature (-10,11).

FORMULA

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

G.f.: x/((1 - x)*(1 + 11*x)). - Vincenzo Librandi, Oct 22 2012

a(n) = -10*a(n-1) + 11*a(n-2). - Vincenzo Librandi, Oct 22 2012

E.g.f.: (exp(x) - exp(-11*x))/12. - G. C. Greubel, May 26 2018

MAPLE

a:=n->sum ((-11)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008]

MATHEMATICA

LinearRecurrence[{-10, 11}, {1, -10}, 40] (* Vincenzo Librandi, Oct 22 2012 *)

PROG

(Sage) [gaussian_binomial(n, 1, -11) for n in xrange(1, 18)] # Zerinvary Lajos, May 28 2009

(MAGMA) I:=[1, -10]; [n le 2 select I[n] else -10*Self(n-1) +11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012

(PARI) for(n=1, 30, print1((1-(-11)^n)/12, ", ")) \\ G. C. Greubel, May 26 2018

CROSSREFS

Cf. A077925, A014983, A014985, A014986, A014987, A014989, A014990, A014991, A014992, A014994. - Zerinvary Lajos, Dec 16 2008

Sequence in context: A087545 A078252 * A015592 A122574 A176736 A084031

Adjacent sequences:  A014990 A014991 A014992 * A014994 A014995 A014996

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Better name from Ralf Stephan, Jul 14 2013

STATUS

approved

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Last modified August 16 06:22 EDT 2018. Contains 313782 sequences. (Running on oeis4.)