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 A117188 Expansion of (1-x^2)/(1+x^2+x^4). 3
 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Periodic: repeat [1, 0, -2, 0, 1, 0]. Minton mentions that the subsequence a(2^i), i >= 1, oscillates between -2 and 1 (and does not converge 2-adically). - N. J. A. Sloane, Jul 09 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Gregory T. Minton, Linear recurrence sequences satisfying congruence conditions, Proc. Amer. Math. Soc. 142 (2014), no. 7, 2337--2352. MR3195758. See Example 6.13. - N. J. A. Sloane, Jul 09 2014 Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1). FORMULA G.f.: (1-2*x^2+x^4)/(1-x^6). a(n) = (1/6)*(-(n mod 6)+((n+1) mod 6)-((n+2) mod 6)-2*((n+3) mod 6)+2*((n+4) mod 6)+((n+5) mod 6)). - Paolo P. Lava, Jun 01 2007 a(n) = (1+(-1)^n)/(-2+4^(floor((n-1)/3)-2*floor((n-1)/6))). - Tani Akinari, Aug 02 2013 a(n) = -a(n-2) - a(n-4) for n >= 4. - N. J. A. Sloane, Jul 09 2014 From Wesley Ivan Hurt, Jun 23 2016: (Start) a(n) = a(n-6) for n>5. a(n) = cos(n*Pi/2) * (cos(n*Pi/6) + sqrt(3)*sin(n*Pi/6)). (End) E.g.f.: cos(sqrt(3)*x/2)*cosh(x/2) - sqrt(3)*sin(sqrt(3)*x/2)*sinh(x/2). - Ilya Gutkovskiy, Jun 27 2016 MAPLE A117188:=n->[1, 0, -2, 0, 1, 0][(n mod 6)+1]: seq(A117188(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016 MATHEMATICA PadRight[{}, 100, {1, 0, -2, 0, 1, 0}] (* Wesley Ivan Hurt, Jun 23 2016 *) PROG (MAGMA) &cat [[1, 0, -2, 0, 1, 0]^^20]; // Wesley Ivan Hurt, Jun 23 2016 CROSSREFS Row sums of A117185. Sequence in context: A016253 A286998 A097796 * A276084 A230403 A248908 Adjacent sequences:  A117185 A117186 A117187 * A117189 A117190 A117191 KEYWORD sign,easy AUTHOR Paul Barry, Mar 01 2006 STATUS approved

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Last modified May 24 17:16 EDT 2019. Contains 323533 sequences. (Running on oeis4.)