OFFSET
0,2
COMMENTS
If we drop 1 and start with 2 this is the Lucas sequence V(-1,-1). G.f.: (2+x)/(1+x-x^2). In this case a(n) is also the trace of A^(-n), where A is the Fibomatrix ((1,1), (1,0)). - Mario Catalani (mario.catalani(AT)unito.it), Aug 17 2002
The positive sequence with g.f. (1+x-2x^2)/(1-x-x^2) gives the diagonal sums of the Riordan array (1+2x,x/(1-x)). - Paul Barry, Jul 18 2005
Pisano period lengths: 1, 3, 8, 6, 4, 24, 16, 12, 24, 12, 10, 24, 28, 48, 8, 24, 36, 24, 18, 12, .... (is this A106291?). - R. J. Mathar, Aug 10 2012
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..4771 (terms 0..500 from T. D. Noe)
Tanya Khovanova, Recursive Sequences
Kai Wang, Fibonacci Numbers And Trigonometric Functions Outline, (2019).
Q. Wang, On generalized Lucas sequences, Contemp. Math. 531 (2010) 127-141, Table 2 (k=2).
Wikipedia, Lucas sequence
Index entries for linear recurrences with constant coefficients, signature (-1,1).
FORMULA
a(n) = (-1)^(n-1) * A000204(n-1).
O.g.f.: (3*x+1)/(1+x-x^2). - Len Smiley, Dec 02 2001
EXAMPLE
a(6) = a(4)-a(5) = -4 - 7 = -11.
MATHEMATICA
LinearRecurrence[{-1, 1}, {1, 2}, 40] (* Harvey P. Dale, Nov 22 2011 *)
PROG
(Haskell)
a061084 n = a061084_list !! n
a061084_list = 1 : 2 : zipWith (-) a061084_list (tail a061084_list)
-- Reinhard Zumkeller, Feb 01 2014
(PARI) a(n)=([0, 1; 1, -1]^n*[1; 2])[1, 1] \\ Charles R Greathouse IV, Feb 09 2017
CROSSREFS
KEYWORD
sign,easy,nice
AUTHOR
Ulrich Schimke (ulrschimke(AT)aol.com)
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved