OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=9, a(1)=100, a(2)=289. - Harvey P. Dale, Jul 19 2014
G.f.: (9 + 73*x + 16*x^2)/(1-x)^3. - Harvey P. Dale, Jul 19 2014
E.g.f.: (9 + 91*x + 49*x^2)*exp(x). - G. C. Greubel, Oct 17 2023
Sum_{n>=0} 1/a(n) = psi'(3/7)/49 = 0.13147479209450263890925... - R. J. Mathar, May 07 2024
MATHEMATICA
(7*Range[0, 40]+3)^2 (* or *) LinearRecurrence[{3, -3, 1}, {9, 100, 289}, 40] (* Harvey P. Dale, Jul 19 2014 *)
PROG
(Magma) [(7*n+3)^2: n in [0..35]]; // Vincenzo Librandi, Jul 14 2011
(PARI) a(n)=(7*n+3)^2 \\ Charles R Greathouse IV, Jun 17 2017
(SageMath) [(7*n+3)^2 for n in range(40)] # G. C. Greubel, Oct 17 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved