A116697 - OEIS

%I #22 Oct 13 2018 09:14:12

%S 1,1,-2,2,-2,5,-9,13,-20,34,-56,89,-143,233,-378,610,-986,1597,-2585,

%T 4181,-6764,10946,-17712,28657,-46367,75025,-121394,196418,-317810,

%U 514229,-832041,1346269,-2178308,3524578,-5702888

%N a(n) = -a(n-1) - a(n-3) + a(n-4).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 0, -1, 1).

%F G.f.: -(1 + 2*x - x^2 + x^3)/((1 + x^2)*(x^2 - x - 1)).

%F a(2n+1) = F(2n+1) = A001519(n).

%F a(2*n) = - A128535(n+1). - _Reinhard Zumkeller_, Feb 25 2011

%F a(n) = A056594(n) - (-1)^n*A000045(n). - _Bruno Berselli_, Feb 26 2011

%t LinearRecurrence[{-1,0,-1,1},{1,1,-2,2},40] (* _Harvey P. Dale_, Nov 04 2011 *)

%o (Haskell)

%o a116697 n = a116697_list !! n

%o a116697_list = [1,1,-2,2]

%o                ++ (zipWith (-) a116697_list

%o                                $ zipWith (+) (tail a116697_list)

%o                                              (drop 3 a116697_list))

%o a128535_list = 0 : (map negate $ map a116697 [0,2..])

%o a001519_list = 1 : map a116697 [1,3..]

%o a186679_list = zipWith (-) (tail a116697_list) a116697_list

%o a128533_list = map a186679 [0,2..]

%o a081714_list = 0 : (map negate $ map a186679 [1,3..])

%o a075193_list = 1 : -3 : (zipWith (+) a186679_list $ drop 2 a186679_list)

%o -- _Reinhard Zumkeller_, Feb 25 2011

%Y Cf. A006498, A115008, A116698, A116699.

%Y Cf. A186679 (first differences).

%K easy,nice,sign

%O 0,3

%A _Creighton Dement_, Feb 23 2006