OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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
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 *)
PROG
(Magma) [(5*n^2 + 5*n - 6)/2: n in [1..50]]; // Vincenzo Librandi, Sep 13 2013
(PARI) a(n)=(5*n^2+5*n-6)/2 \\ Charles R Greathouse IV, May 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 08 2009
STATUS
approved