A142600 - OEIS

%I #18 Sep 11 2022 06:21:27

%S 3,45,6,165,63,357,30,621,195,957,72,1365,399,1845,132,2397,675,3021,

%T 210,3717,1023,4485,306,5325,1443,6237,420,7221,1935,8277,552,9405,

%U 2499,10605,702,11877,3135,13221,870,14637,3843,16125,1056,17685,4623,19317

%N Third trisection of A061037.

%H G. C. Greubel, <a href="/A142600/b142600.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

%F 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

%F Sum_{n>=1} 1/a(n) = 11*log(3)/16 - 5*Pi/(48*sqrt(3)) + 1/12. - _Amiram Eldar_, Sep 11 2022

%t Table[Numerator[(n-2)*(n+2)/(4*n^2)],{n,4,100,3}] (* _Vaclav Kotesovec_, Oct 15 2014 *)

%t 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 *)

%o (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

%o (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

%Y Cf. A061037, A174325.

%K nonn,easy

%O 1,1

%A _Paul Curtz_, Sep 23 2008

%E Edited by _N. J. A. Sloane_, Jan 04 2009

%E More terms from _Colin Barker_, Oct 15 2014