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

Author

Paul Curtz, Sep 23 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A061037, A174325.

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