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
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
KEYWORD
sign,easy
AUTHOR
Amarnath Murthy, Aug 01 2005
EXTENSIONS
Corrected and extended by Emeric Deutsch, Aug 08 2005
STATUS
approved