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 A084056 a(n) = -a(n-1) + a(n-2) + a(n-3), with a(0)=0, a(1)=1, a(2)=-3. 4
 0, 1, -3, 4, -6, 7, -9, 10, -12, 13, -15, 16, -18, 19, -21, 22, -24, 25, -27, 28, -30, 31, -33, 34, -36, 37, -39, 40, -42, 43, -45, 46, -48, 49, -51, 52, -54, 55, -57, 58, -60, 61, -63, 64, -66, 67, -69, 70, -72, 73, -75, 76, -78, 79, -81, 82, -84, 85, -87, 88, -90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-1,1,1). FORMULA a(n) = (1/4) * ((1-6*n) * (-1)^n - 1). G.f.: (x-2*x^2)/((1+x)*(1-x^2)). a(n) = 2*a(n-2) - a(n-4) = -(-1)^n * A032766(n) = A001057(n) - 2*A001057(n-1). - Ralf Stephan, Aug 18 2013 a(n) = (2n - 1 - floor((n-1)/2)) * (-1)^(n-1). - Wesley Ivan Hurt, Nov 10 2013 MAPLE A084056:=n->((1-6*n) * (-1)^n - 1)/4; seq(A084056(n), n=0..100); # Wesley Ivan Hurt, Nov 10 2013 MATHEMATICA Table[((1 - 6n)(-1)^n - 1)/4, {n, 0, 100}] (* Wesley Ivan Hurt, Nov 10 2013 *) LinearRecurrence[{-1, 1, 1}, {0, 1, -3}, 101] (* T. D. Noe, Nov 11 2013 *) PROG (Magma) [((1-6*n)*(-1)^n-1)/4 : n in [0..100]]; // Zaki Khandaker, Jun 21 2015 (PARI) concat(0, Vec(x*(2*x-1)/((x-1)*(x+1)^2) + O(x^100))) \\ Colin Barker, Jun 21 2015 CROSSREFS Cf. A032766 (absolute values). Sequence in context: A185543 A026322 A049624 * A032766 A189935 A329987 Adjacent sequences: A084053 A084054 A084055 * A084057 A084058 A084059 KEYWORD easy,sign AUTHOR Paul Barry, May 09 2003 EXTENSIONS Definition fixed by Ralf Stephan, Aug 18 2013 STATUS approved

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Last modified June 1 17:57 EDT 2023. Contains 363076 sequences. (Running on oeis4.)