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A116697
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a(n) = -a(n-1)-a(n-3)+a(n-4).
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(2n+1) = F(2n+1) = A001519(n).
a(2*n) = - A128535(n+1). -- Reinhard Zumkeller, Feb 25 2011
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FORMULA
| G.f. -(1+2*x-x^2+x^3)/((1+x^2)*(x^2-x-1))
a(n) = A056594(n)-(-1)^n*A000045(n). - Bruno Berselli, Feb 26 2011
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MATHEMATICA
| LinearRecurrence[{-1, 0, -1, 1}, {1, 1, -2, 2}, 40] (* From Harvey P. Dale, Nov 04 2011 *)
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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
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CROSSREFS
| Cf. A006498, A115008, A116698, A116699.
Cf. A186679 (first differences).
Sequence in context: A039886 A109523 A008295 * A014244 A059814 A079443
Adjacent sequences: A116694 A116695 A116696 * A116698 A116699 A116700
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KEYWORD
| easy,nice,sign
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Feb 23 2006
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