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Search: id:A091337
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| A091337 |
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a(n) = (2/n), where (k/n) is the Kronecker symbol. |
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+0
2
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| 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sinh(1) in 'reflected factorial' base is 1.01010101010101010101010101010101010101010101... see A073097 for Cosh(1) - (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 2005)
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LINKS
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Eric Weisstein's World of Mathematics, Kronecker Symbol
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FORMULA
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G.f. x(1-x^2)/(1+x^4).
Transform of Pell numbers A000129 by the Riordan array A102587. - Paul Barry, Jul 14 2005
a(n)=-a(n+4)=a(-n). a(2n)=0.
a(n) = -(1/8)*[n mod 8-(n+1) mod 8+(n+2) mod 8+(n+3) mod 8-(n+4) mod 8+(n+5) mod 8-(n+6) mod 8-(n+7) mod 8] with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Oct 09 2006
Euler transform of length 8 sequence [ 0, -1, 0, -1, 0, 0, 0, 1]. - Michael Somos Jul 17 2009
a(n) is multiplicative with a(2^e) = 0^e, a(p^e) = 1 if p == 1, 7 (mod 8), a(p^e) = (-1)^e if p == 3, 5 (mod 8). - Michael Somos Jul 17 2009
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EXAMPLE
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x - x^3 - x^5 + x^7 + x^9 - x^11 - x^13 + x^15 + x^17 - x^19 - x^21 + ...
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PROGRAM
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(PARI) a(n)=(n%2)*(-1)^((n+1)\4) /* Michael Somos Sep 10 2005 */
(PARI) a(n)=kronecker(2, n) /* Michael Somos Sep 10 2005 */
(PARI) {a(n) = [0, 1, 0, -1, 0, -1, 0, 1][n%8 + 1]} /* Michael Somos Jul 17 2009 */
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CROSSREFS
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Sequence in context: A166698 A101455 A056594 this_sequence A059841 A071022 A071025
Adjacent sequences: A091334 A091335 A091336 this_sequence A091338 A091339 A091340
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KEYWORD
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sign,mult
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Dec 30, 2003
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