A116697 a(n) = -a(n-1) - a(n-3) + a(n-4).

1, 1, -2, 2, -2, 5, -9, 13, -20, 34, -56, 89, -143, 233, -378, 610, -986, 1597, -2585, 4181, -6764, 10946, -17712, 28657, -46367, 75025, -121394, 196418, -317810, 514229, -832041, 1346269, -2178308, 3524578, -5702888

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (-1, 0, -1, 1).

Formula

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

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

a(2*n) = - A128535(n+1). - Reinhard Zumkeller, Feb 25 2011

a(n) = A056594(n) - (-1)^n*A000045(n). - Bruno Berselli, Feb 26 2011

Mathematica

LinearRecurrence[{-1, 0, -1, 1}, {1, 1, -2, 2}, 40] (* Harvey P. Dale, Nov 04 2011 *)

Prog

(Haskell)
a116697 n = a116697_list !! n
a116697_list = [1, 1, -2, 2]
               ++ (zipWith (-) a116697_list
                               $ zipWith (+) (tail a116697_list)
                                             (drop 3 a116697_list))
a128535_list = 0 : (map negate $ map a116697 [0, 2..])
a001519_list = 1 : map a116697 [1, 3..]
a186679_list = zipWith (-) (tail a116697_list) a116697_list
a128533_list = map a186679 [0, 2..]
a081714_list = 0 : (map negate $ map a186679 [1, 3..])
a075193_list = 1 : -3 : (zipWith (+) a186679_list $ drop 2 a186679_list)
-- Reinhard Zumkeller, Feb 25 2011

Crossrefs

Cf. A006498, A115008, A116698, A116699.

Cf. A186679 (first differences).

Sequence in context: A339613 A008295 A216694 * A014244 A216634 A208054

Adjacent sequences: A116694 A116695 A116696 * A116698 A116699 A116700

Keyword

easy,nice,sign

Author

Creighton Dement, Feb 23 2006

Status

approved