OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n*(n + 22).
a(n) = 2*n + a(n-1) + 21 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=23, a(2)=48, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 02 2012
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(22)/22 = A001008(22)/A102928(22) = 19093197/113809696, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 156188887/5121436320. (End)
From G. C. Greubel, Mar 14 2022: (Start)
G.f.: x*(23 - 21*x)/(1-x)^3.
E.g.f.: x*(23 + x)*exp(x). (End)
EXAMPLE
a(1)=2*1+0+21=23; a(2)=2*2+23+21=48; a(3)=2*3+48+21=75. - Vincenzo Librandi, Aug 03 2010
MATHEMATICA
Table[n(n+22), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 23, 48}, 50] (* Harvey P. Dale, May 02 2012 *)
PROG
(PARI) a(n)=n*(n+22) \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [n*(n+22) for n in (0..50)] # G. C. Greubel, Mar 14 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved