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 A077966 Expansion of 1/(1+2*x^2). 8
 1, 0, -2, 0, 4, 0, -8, 0, 16, 0, -32, 0, 64, 0, -128, 0, 256, 0, -512, 0, 1024, 0, -2048, 0, 4096, 0, -8192, 0, 16384, 0, -32768, 0, 65536, 0, -131072, 0, 262144, 0, -524288, 0, 1048576, 0, -2097152, 0, 4194304, 0, -8388608, 0, 16777216, 0, -33554432, 0, 67108864, 0, -134217728, 0, 268435456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database. Inverse binomial transform of A087455. - Philippe Deléham, Dec 02 2008 Pisano period lengths: 1, 1, 2, 1, 8, 2, 12, 1, 6, 8, 10, 2, 24, 12, 8, 1, 16, 6, 18, 8,... - R. J. Mathar, Aug 10 2012 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,-2). FORMULA a(n) = (1+(-1)^n)*(-2)^(n/2)/2. - R. J. Mathar, Apr 23 2009 a(n) = ((n+1) mod 2 )*(-2)^floor((n+1)/2). - Wesley Ivan Hurt, Apr 06 2014 E.g.f.: cos(sqrt(2)*x). - G. C. Greubel, Jun 24 2019 MAPLE A077966:=n->(1+(-1)^n)*(-2)^(n/2)/2; seq(A077966(n), n=0..50); # Wesley Ivan Hurt, Apr 02 2014 MATHEMATICA CoefficientList[Series[1/(1 + 2*x^2), {x, 0, 60}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *) LinearRecurrence[{0, -2}, {1, 0}, 60] (* G. C. Greubel, Jun 24 2019 *) PROG (Sage) [lucas_number1(n, 0, 2) for n in range(1, 60)] # Zerinvary Lajos, Jul 16 2008 (PARI) Vec(1/(1+2*x^2)+O(x^60)) \\ Charles R Greathouse IV, Sep 24 2012 (PARI) for(n=0, 51, print1(imag(quadgen(-8)^(n+1)), ", ")) \\ Arkadiusz Wesolowski, Dec 26 2012 (Magma) I:=[1, 0]; [n le 2 select I[n] else -2*Self(n-2): n in [1..60]]; // G. C. Greubel, Jun 24 2019 (GAP) a:=[1, 0];; for n in [3..60] do a[n]:=-2*a[n-2]; od; a; # G. C. Greubel, Jun 24 2019 CROSSREFS Cf. A000079, A077957. Sequence in context: A194795 A131575 A077957 * A275670 A021102 A021053 Adjacent sequences: A077963 A077964 A077965 * A077967 A077968 A077969 KEYWORD sign,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified September 29 00:22 EDT 2023. Contains 365739 sequences. (Running on oeis4.)