OFFSET
5,3
COMMENTS
It is conjectured that this sequence (with a different offset) and A038360 are the same.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 5..1000
P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998).
M. Waldschmidt, Lectures on Multiple Zeta Values (IMSC2011).
Index entries for linear recurrences with constant coefficients, signature (2,1,-1,-2)
FORMULA
G.f.: -x^6*(-1-x+x^2) / ( (2*x-1)*(x^3+x^2-1) ). - R. J. Mathar, Sep 16 2012
a(n) = 2*a(n-1)+a(n-2)-a(n-3)-2*a(n-4). - Vincenzo Librandi, Mar 11 2013
MATHEMATICA
CoefficientList[Series[-x (-1 - x + x^2)/((2 x - 1) (x^3 + x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 11 2013 *)
LinearRecurrence[{2, 1, -1, -2}, {0, 1, 3, 6}, 40] (* Harvey P. Dale, Aug 22 2021 *)
PROG
(Magma) I:=[0, 1, 3, 6]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-2)-Self(n-3)-2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Mar 11 2013
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -2, -1, 1, 2]^(n-5)*[0; 1; 3; 6])[1, 1] \\ Charles R Greathouse IV, Sep 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 14 2012
STATUS
approved