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A127365
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Signed repeated natural numbers.
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3
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0, 0, -1, -1, 2, 2, -3, -3, 4, 4, -5, -5, 6, 6, -7, -7, 8, 8, -9, -9, 10, 10, -11, -11, 12, 12, -13, -13, 14, 14, -15, -15, 16, 16, -17, -17, 18, 18, -19, -19, 20, 20, -21, -21, 22, 22, -23, -23, 24, 24, -25, -25, 26, 26, -27, -27, 28, 28, -29, -29, 30, 30, -31, -31
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OFFSET
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0,5
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COMMENTS
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Hankel transform of A093387.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,-2,0,-1)
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FORMULA
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G.f.: -x^2*(1+x)/(1+x^2)^2.
a(n) = floor(n/2)*(sin(n*Pi/2) + cos(n*Pi/2)).
a(n) = floor(n/2)*(-1)^floor(n/2) = A004526(n)*(-1)^A004526(n). - Wesley Ivan Hurt, Dec 10 2013
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MAPLE
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A127365:=n->floor(n/2)*(-1)^floor(n/2); seq(A127365(n), n=0..100); # Wesley Ivan Hurt, Nov 30 2013
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MATHEMATICA
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With[{c=Table[n (-1)^n, {n, 0, 30}]}, Riffle[c, c]] (* Harvey P. Dale, Jul 21 2013 *)
LinearRecurrence[{0, -2, 0, -1}, {0, 0, -1, -1}, 100] (* Vincenzo Librandi, Nov 18 2018 *)
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PROG
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(MAGMA) [(n div 2)*(-1)^(n div 2): n in [0..100]]; // Vincenzo Librandi, Nov 18 2018
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CROSSREFS
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Cf. A004526.
Sequence in context: A168050 A065033 A001057 * A130472 A076938 A080513
Adjacent sequences: A127362 A127363 A127364 * A127366 A127367 A127368
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, Jan 11 2007
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STATUS
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approved
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