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A104537
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Expansion of g.f.: (1+x)/(1+2*x+4x^2).
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4
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1, -1, -2, 8, -8, -16, 64, -64, -128, 512, -512, -1024, 4096, -4096, -8192, 32768, -32768, -65536, 262144, -262144, -524288, 2097152, -2097152, -4194304, 16777216, -16777216, -33554432, 134217728, -134217728, -268435456, 1073741824, -1073741824, -2147483648, 8589934592
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OFFSET
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0,3
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COMMENTS
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a(n+1) is the Hankel transform of C(2n,n)-C(2n+2,n+1). - Paul Barry, Mar 14 2008
a(n+1) is the Hankel transform of C(2n,n)-2*C(n)=((n-1)/(n+1))*C(2n,n), where C(n)=A000108(n). - Paul Barry, Mar 14 2008
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LINKS
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FORMULA
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G.f.: (1+x)/(1+2*x+4x^2).
a(n) = -2*a(n-1) - 4*a(n-2).
a(n) = 2^n*cos(2*Pi*n/3).
a(n) = (3^n/2^n)*Product_{i=1..n} (1/3 - tan((i-1/2)*Pi/(2*n))^2). - Gerry Martens, May 26 2011
G.f.: G(0)/2, where G(k) = 1 + 1/(1 - x*(3*k+1)/(x*(3*k+4) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 26 2013
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 + x) / (1 + 2 x + 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 16 2014 *)
LinearRecurrence[{-2, -4}, {1, -1}, 40] (* Harvey P. Dale, Dec 02 2019 *)
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PROG
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(Magma) I:=[1, -1]; [n le 2 select I[n] else -2*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Nov 16 2014
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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