OFFSET
1,2
COMMENTS
q-integers for q = -5.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-5, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 27 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-4,5).
FORMULA
a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
G.f.: x/((1-x)*(1+5*x)). - Bruno Berselli, Dec 07 2011
a(n) = -4*a(n-1) + 5*a(n-2). - Vincenzo Librandi, Jun 19 2012
E.g.f.: (exp(x) - exp(-5*x))/6. - G. C. Greubel, May 26 2018
MAPLE
a:=n->sum ((-5)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
MATHEMATICA
LinearRecurrence[{-4, 5}, {1, -4}, 30] (* Vincenzo Librandi, Jun 19 2012 *)
PROG
(Sage) [gaussian_binomial(n, 1, -5) for n in range(1, 22)] # Zerinvary Lajos, May 28 2009
(PARI) a(n)=(1-(-5)^n)/6 \\ Charles R Greathouse IV, Dec 07 2011
(Magma) I:=[1, -4]; [n le 2 select I[n] else -4*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 19 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Better name from Ralf Stephan, Jul 14 2013
STATUS
approved