OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
FORMULA
G.f.: 3*x*(x^11 -7*x^9 -5*x^8 -42*x^7 -4*x^6 -74*x^5 -18*x^4 -55*x^3 -2*x^2 -15*x -1) / ((x -1)^3*(x +1)^3*(x^2 +1)^3). - Colin Barker, Oct 15 2014
Sum_{n>=1} 1/a(n) = 11*log(3)/16 - 5*Pi/(48*sqrt(3)) + 1/12. - Amiram Eldar, Sep 11 2022
MATHEMATICA
Table[Numerator[(n-2)*(n+2)/(4*n^2)], {n, 4, 100, 3}] (* Vaclav Kotesovec, Oct 15 2014 *)
Rest[CoefficientList[Series[3*x*(x^11 -7*x^9 -5*x^8 -42*x^7 -4*x^6 -74*x^5 -18*x^4 -55*x^3 -2*x^2 -15*x -1)/((x-1)^3*(x+1)^3*(x^2+1)^3), {x, 0, 50}], x]] (* G. C. Greubel, Sep 19 2018 *)
PROG
(PARI) Vec(3*x*(x^11-7*x^9-5*x^8-42*x^7-4*x^6-74*x^5-18*x^4-55*x^3 -2*x^2-15*x-1)/((x-1)^3*(x+1)^3*(x^2+1)^3) + O(x^100)) \\ Colin Barker, Oct 15 2014
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(3*x*(x^11 -7*x^9 -5*x^8 -42*x^7 -4*x^6 -74*x^5 -18*x^4 -55*x^3 -2*x^2 -15*x -1)/((x-1)^3*(x+1)^3*(x^2+1)^3))); // G. C. Greubel, Sep 19 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 23 2008
EXTENSIONS
Edited by N. J. A. Sloane, Jan 04 2009
More terms from Colin Barker, Oct 15 2014
STATUS
approved