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 A104537 Expansion of g.f.: (1+x)/(1+2*x+4x^2). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS Index entries for linear recurrences with constant coefficients, signature (-2,-4). FORMULA 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) = Sum_{k, 0<=k<=n} A098158(n,k)*(-1)^k*3^(n-k). - Philippe Deléham, Nov 14 2008 a(n) = (1/2)*{[ -1+I*sqrt(3)]^n+[ -1-I*sqrt(3)]^n}, with n>=0. - Paolo P. Lava, Nov 19 2008 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 a(n) = b(n)+b(n-1) where b(n) = 2^n*A049347(n). - R. J. Mathar, May 21 2019 MAPLE A104537:=n->2^n*cos(2*Pi*n/3): seq(A104537(n), n=0..40); # Wesley Ivan Hurt, Nov 16 2014 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000108, A098158. Sequence in context: A290378 A138230 A128018 * A019240 A269510 A093907 Adjacent sequences:  A104534 A104535 A104536 * A104538 A104539 A104540 KEYWORD easy,sign,changed AUTHOR Paul Barry, Mar 13 2005 STATUS approved

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Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)