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
From Vincenzo Librandi, Feb 08 2012: (Start)
900*a(n) + 1 = (450*n - 199)^2.
G.f.: (44 - 62*x + 468*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
E.g.f.: (44 + 26*x + 225*x^2)*exp(x). - G. C. Greubel, Jun 10 2021
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {44, 70, 546}, 40] (* Vincenzo Librandi, Feb 08 2012 *)
PROG
(PARI) a(n)=225*n^2-199*n+44 \\ Charles R Greathouse IV, Dec 23 2011
(Magma) I:=[44, 70, 546]; [n le 3 select I[n] else 3*Self(n-1) -3*Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 08 2012
(Sage) [225*n^2 -199*n +44 for n in (0..40)] # G. C. Greubel, Jun 10 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 16 2009
EXTENSIONS
Offset corrected by R. J. Mathar, Aug 18 2009
STATUS
approved