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A038608
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a(n) = n*(-1)^n.
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20
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0, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 34, -35, 36, -37, 38, -39, 40, -41, 42, -43, 44, -45, 46, -47, 48, -49, 50, -51, 52, -53, 54, -55, 56, -57, 58, -59, 60, -61, 62, -63, 64, -65
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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a(n) is the determinant of the (n+1) X (n+1) matrix with 0's in the main diagonal and 1's elsewhere. - Franz Vrabec, Dec 01 2007
Pisano period lengths: 1, 2, 6, 4, 10, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, ... (is this A066043?). - R. J. Mathar, Aug 10 2012
a(n) is the determinant of the (n+1) X (n+1) matrix whose i-th row, j-th column entry is the value of the cubic residue symbol ((j-i)/p) where p is a prime of the form 3k+2 and n < p. - Ryan Wood, Nov 09 2017
a(n-1) is the difference in the number of even minus odd parity derangements (permutations with no fixed points) in symmetric group S_n. - Julian Hatfield Iacoponi, Aug 01 2024
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LINKS
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FORMULA
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G.f.: -x/(1+x)^2.
E.g.f: -x*exp(-x).
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MAPLE
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MATHEMATICA
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Table[If[EvenQ[n], n, -n], {n, 0, 70}] (* Harvey P. Dale, Jan 17 2022 *)
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PROG
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(Haskell)
a038608 n = n * (-1) ^ n
a038608_list = [0, -1] ++ map negate
(zipWith (+) a038608_list (map (* 2) $ tail a038608_list))
(Python)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jul 1998
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EXTENSIONS
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STATUS
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approved
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