OFFSET
1,2
COMMENTS
q-integers for q=-12.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..900
Index entries for linear recurrences with constant coefficients, signature (-11,12).
FORMULA
a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
G.f.: x/((1 - x)*(1 + 12*x)). - Vincenzo Librandi, Oct 22 2012
a(n) = -11*a(n-1) + 12*a(n-2). - Vincenzo Librandi, Oct 22 2012
E.g.f.: (exp(x) - exp(-12*x))/13. - G. C. Greubel, May 26 2018
MAPLE
a:=n->sum ((-12)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
MATHEMATICA
LinearRecurrence[{-11, 12}, {1, -11}, 30] (* Vincenzo Librandi, Oct 22 2012 *)
PROG
(Sage) [gaussian_binomial(n, 1, -12) for n in range(1, 18)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -11]; [n le 2 select I[n] else -11*Self(n-1)+12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012
(PARI) a(n)=(1-(-12)^n)/13 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Better name from Ralf Stephan, Jul 14 2013
STATUS
approved