A142600 Third trisection of A061037.
3, 45, 6, 165, 63, 357, 30, 621, 195, 957, 72, 1365, 399, 1845, 132, 2397, 675, 3021, 210, 3717, 1023, 4485, 306, 5325, 1443, 6237, 420, 7221, 1935, 8277, 552, 9405, 2499, 10605, 702, 11877, 3135, 13221, 870, 14637, 3843, 16125, 1056, 17685, 4623, 19317
Offset: 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).
Programs
-
Magma
m:=25; R
:=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 -
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 *) -
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
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
Extensions
Edited by N. J. A. Sloane, Jan 04 2009
More terms from Colin Barker, Oct 15 2014