A166151 a(n) = (5*n^2 + 5*n - 6)/2.

2, 12, 27, 47, 72, 102, 137, 177, 222, 272, 327, 387, 452, 522, 597, 677, 762, 852, 947, 1047, 1152, 1262, 1377, 1497, 1622, 1752, 1887, 2027, 2172, 2322, 2477, 2637, 2802, 2972, 3147, 3327, 3512, 3702, 3897, 4097, 4302, 4512, 4727, 4947, 5172, 5402, 5637

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Magma

[(5*n^2 + 5*n - 6)/2: n in [1..50]]; // Vincenzo Librandi, Sep 13 2013

Mathematica

Table[(5 n^2 + 5 n - 6)/2, {n, 50}] (* or *) CoefficientList[Series[(- 2 - 6 x + 3 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3,-3,1},{2,12,27}, 50] (* G. C. Greubel, May 01 2016 *)

PARI

a(n)=(5*n^2+5*n-6)/2 \\ Charles R Greathouse IV, May 02 2016

Formula

From R. J. Mathar, Oct 14 2009: (Start)

a(n) = 5*n*(n+1)/2 - 3.

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-2-6*x+3*x^2)/(x-1)^3. (End)

E.g.f.: (1/2)*(5*x^2 + 10*x - 6)*exp(x) + 6. - G. C. Greubel, May 01 2016

Sum_{n>=1} 1/a(n) = 1/3 + (2*Pi/sqrt(145))*tan(sqrt(29/5)*Pi/2). - Amiram Eldar, Feb 20 2023