OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = (1/2)*(2 + 47*n + 47*n^2).
From Colin Barker, Jul 27 2013: (Start)
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: (1 + 45*x + x^2)/(1-x)^3. (End)
E.g.f.: (1/2)*(2 + 94*x + 47*x^2)*exp(x). - G. C. Greubel, Feb 05 2024
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 48, 142}, 70] (* Vincenzo Librandi, Sep 09 2016 *)
PROG
(Magma) [1+(47/2)*n+(47/2)*n^2: n in [0..50]]; // Vincenzo Librandi, Sep 09 2016
(PARI) a(n)=47*n*(n+1)/2+1 \\ Charles R Greathouse IV, Jun 17 2017
(SageMath) [1+47*binomial(n+1, 2) for n in range(51)] # G. C. Greubel, Feb 05 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 06 2007, based on a suggestion from an unknown correspondent in 2004.
STATUS
approved