OFFSET
1,2
COMMENTS
First differences are in A008592.
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
a(n) = a(n-1) + 10*n (with a(1)=1).
G.f.: x*(1+18*x-9*x^2)/(1-x)^3. - Vincenzo Librandi, Sep 13 2013
From G. C. Greubel, May 01 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: (5*x^2 + 10*x - 9)*exp(x) + 9. (End)
Sum_{n>=1} 1/a(n) = 1/9 + (Pi/sqrt(205))*tan(sqrt(41/5)*Pi/2). - Amiram Eldar, Feb 20 2023
MAPLE
MATHEMATICA
Table[(5 n^2 + 5 n - 9), {n, 50}] (* or *) CoefficientList[Series[(1 + 18 x - 9 x^2)/(1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{3, -3, 1}, {1, 21, 51}, 50] (* G. C. Greubel, May 01 2016 *)
PROG
(PARI) a(n)=5*n*(n+1)-9 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) [5*n^2+5*n-9: n in [1..45]]; // Vincenzo Librandi, Sep 13 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 08 2009
EXTENSIONS
a(29)-a(45) corrected by Charles R Greathouse IV, Jan 11 2012
New name from Charles R Greathouse IV, Jan 11 2012
STATUS
approved