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 A110422 a(n) = sum( (-1)^(r+1)*(n-r)*r, r = 1..floor(n/2) ). 0
 1, 2, -1, -2, 6, 8, -6, -8, 15, 18, -15, -18, 28, 32, -28, -32, 45, 50, -45, -50, 66, 72, -66, -72, 91, 98, -91, -98, 120, 128, -120, -128, 153, 162, -153, -162, 190, 200, -190, -200, 231, 242, -231, -242, 276, 288, -276, -288, 325, 338, -325, -338, 378, 392, -378, -392, 435, 450, -435, -450, 496, 512, -496, -512, 561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(4n)=-a(4n-2); a(4n+1)=-a(4n-1). If sum in definition is not alternating one obtains A023855. - Emeric Deutsch, Aug 08 2005 LINKS Table of n, a(n) for n=2..66. Index entries for linear recurrences with constant coefficients, signature (2,-4,6,-6,6,-4,2,-1). FORMULA a(2n) = (1/2)n-(-1)^n*(1/2)n^2; a(2n-1) = (1/2)n-(1/4)+(-1)^n*(1/4)(2n^2-2n+1). - Emeric Deutsch, Aug 08 2005 a(n) = (-1)^((2*n-5+(-1)^n)/4)*(2*n^2+1-(-1)^n+4*n*(-1)^((2*n-5+(-1)^n)/4))/16. - Luce ETIENNE, Oct 30 2014 G.f.: x^2*(2*x^3-x^2+1) / ((x-1)^2*(x^2+1)^3). - Colin Barker, Oct 30 2014 EXAMPLE a(8) = -6 because 7*1-6*2+5*3-4*4 = -6. MAPLE a:=n->sum((-1)^(r+1)*(n-r)*r, r=1..floor(n/2)): seq(a(n), n=2..70); # Emeric Deutsch, Aug 08 2005 MATHEMATICA CoefficientList[Series[(2 x^3 - x^2 + 1)/((x - 1)^2 (x^2 + 1)^3), {x, 0, 70}], x] (* Vincenzo Librandi, Oct 30 2014 *) LinearRecurrence[{2, -4, 6, -6, 6, -4, 2, -1}, {1, 2, -1, -2, 6, 8, -6, -8}, 70] (* Harvey P. Dale, Apr 04 2020 *) PROG (PARI) Vec(x^2*(2*x^3-x^2+1)/((x-1)^2*(x^2+1)^3) + O(x^100)) \\ Colin Barker, Oct 30 2014 CROSSREFS Cf. A023855. Sequence in context: A070236 A020825 A259992 * A131804 A307519 A254198 Adjacent sequences: A110419 A110420 A110421 * A110423 A110424 A110425 KEYWORD sign,easy AUTHOR Amarnath Murthy, Aug 01 2005 EXTENSIONS Corrected and extended by Emeric Deutsch, Aug 08 2005 STATUS approved

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Last modified June 23 15:01 EDT 2024. Contains 373651 sequences. (Running on oeis4.)