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 A130778 Period 6: repeat [1, -1, -3, -3, -1, 1]. 1
 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3, -1, 1, 1, -1, -3, -3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS With offset 1, a(n) satisfies the interesting recurrence: a(n+1) = Sum_{k=1..n} binomial(n, k)*(-1)^k*a(k); see Mathematica code below. - John M. Campbell, May 05 2012 LINKS Index entries for linear recurrences with constant coefficients, signature (2,-2,1). FORMULA a(n) = -(1/15)*((n mod 6) + 6*((n+1) mod 6) + 6*((n+2) mod 6) + ((n+3) mod 6) + 4*((n+4) mod 6) + 4*((n+5) mod 6)). - Paolo P. Lava, Jul 18 2007 From Wesley Ivan Hurt, Jun 19 2016: (Start) G.f.: (1-3*x+x^2)/(1-2*x+2*x^2-x^3). a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>2. a(n) = (6*cos(n*Pi/3) - 2*sqrt(3)*sin(n*Pi/3) - 3)/3. (End) MAPLE A130778:=n->[1, -1, -3, -3, -1, 1][(n mod 6)+1]: seq(A130778(n), n=0..100); # Wesley Ivan Hurt, Jun 19 2016 MATHEMATICA Table1 = {1}; a[1] = 1; n = 1; While[n < 314, a[n + 1] = Sum[Binomial[n, k]*(-1)^k*a[k], {k, 1, n}]; AppendTo[Table1, a[n + 1]]; n++]; Print[Table1] (* John M. Campbell, May 05 2012 *) PadRight[{}, 200, {1, -1, -3, -3, -1, 1}] (* Wesley Ivan Hurt, Jun 19 2016 *) PROG (MAGMA) &cat[[1, -1, -3, -3, -1, 1]^^20]; // Wesley Ivan Hurt, Jun 19 2016 CROSSREFS Sequence in context: A059790 A307156 A326057 * A328572 A016554 A046533 Adjacent sequences:  A130775 A130776 A130777 * A130779 A130780 A130781 KEYWORD sign,easy AUTHOR Paul Curtz, Jul 14 2007 STATUS approved

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Last modified April 11 09:24 EDT 2021. Contains 342886 sequences. (Running on oeis4.)