OFFSET
1,2
COMMENTS
q-integers for q = -7.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (-6,7).
FORMULA
a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
a(n) = -6*a(n-1) + 7*a(n-2). - Vincenzo Librandi, Oct 22 2012
From G. C. Greubel, May 26 2018: (Start)
G.f.: x/((1-x)*(1+7*x)).
E.g.f.: (exp(x) - exp(-7*x))/8. (End)
MAPLE
a:=n->sum ((-7)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
MATHEMATICA
LinearRecurrence[{-6, 7}, {1, -6}, 30] (* Vincenzo Librandi, Oct 22 2012 *)
PROG
(Sage) [gaussian_binomial(n, 1, -7) for n in range(1, 21)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -6]; [n le 2 select I[n] else -6*Self(n-1)+7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 2012
(PARI) x='x+O('x^30); Vec(x/((1-x)*(1+7*x))) \\ G. C. Greubel, May 26 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Better name from Ralf Stephan, Jul 14 2013
STATUS
approved