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 A131713 Period 3: repeat [1, -2, 1]. 9
 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Second differences of A131534. Binomial transform of 1, -3, 6, -9, 9, 0 ..., A057083 signed. Nonsimple continued fraction expansion of sqrt(2)-1 = 0.414213562... - R. J. Mathar, Mar 08 2012 LINKS Index entries for linear recurrences with constant coefficients, signature (-1,-1). FORMULA a(n) = b(2*n + 1) where b(n) is multiplicative with b(2^n) = 0^n, b(3^n) = 3 * 0^n - 2, b(p^n) = 1 if p > 3. - Michael Somos, Jan 02 2011 a(n) = {-[(n+1) mod 3]+[(n+2) mod 3]}. - Paolo P. Lava, Oct 02 2007 G.f.: (1-x)/(x^2+x+1). - R. J. Mathar, Nov 14 2007 a(n) = 2*cos((2n+1)*Pi/3). [Jaume Oliver Lafont, Nov 23 2008] a(n) = 1/3*(-1/2-(1/2*I)*sqrt(3))^(-2)*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2+(1/2*I)*sqrt(3))^(-2)*(-1/2+(1/2*I)*sqrt(3))^n+1/3*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2 +(1/2*I)*sqrt(3))^n-2/3*(-1/2-(1/2*I)*sqrt(3))^(-1)*(-1/2-(1/2*I)*sqrt(3))^n-2/3*(-1/2+(1/2*I)*sqrt(3))^(-1)*(-1/2+(1/2*I)*sqrt(3))^n, with I=sqrt(-1). [Paolo P. Lava, Nov 27 2008] a(n) = A117188(2*n). - R. J. Mathar, Jun 13 2011 a(n) + a(n-1) + a(n-2) = 0 for n>1, a(n) = a(n-3) for n>2. - Wesley Ivan Hurt, Jul 01 2016 a(n) = (1/4^n) * Sum_{k = 0..n} binomial(2*n+1,2*k)*(-3)^k. - Peter Bala, Feb 06 2019 MAPLE seq(op([1, -2, 1]), n=0..50); # Wesley Ivan Hurt, Jul 01 2016 MATHEMATICA f[n_] := If[ Mod[n, 3] == 1, -2, 1]; Array[f, 105, 0] CoefficientList[Series[(1 - x)/(1 + x + x^2), {x, 0, 104}], x] PadRight[{}, 120, {1, -2, 1}] (* Harvey P. Dale, Jan 25 2014 *) PROG (PARI) a(n)=[1, -2, 1][1+n%3] \\ Jaume Oliver Lafont, Mar 24 2009 (PARI) a(n)=1-3*(n%3==1) \\ Jaume Oliver Lafont, Mar 24 2009 (MAGMA) &cat [[1, -2, 1]^^30]; // Wesley Ivan Hurt, Jul 01 2016 CROSSREFS Cf. A057083, A061347, A131534. Sequence in context: A100051 A281727 A122876 * A100063 A057079 A132419 Adjacent sequences:  A131710 A131711 A131712 * A131714 A131715 A131716 KEYWORD sign,easy,less AUTHOR Paul Curtz, Sep 14 2007 EXTENSIONS Corrected and extended by Michael Somos, Jan 02 2011 STATUS approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)