A156810 a(n) = 225*n^2 - 251*n + 70.

70, 44, 468, 1342, 2666, 4440, 6664, 9338, 12462, 16036, 20060, 24534, 29458, 34832, 40656, 46930, 53654, 60828, 68452, 76526, 85050, 94024, 103448, 113322, 123646, 134420, 145644, 157318, 169442, 182016, 195040, 208514, 222438, 236812, 251636

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 - 251)^2.

G.f.: (70 - 166*x + 546*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

E.g.f.: (70 - 26*x + 225*x^2)*exp(x). - G. C. Greubel, Jun 10 2021

Mathematica

LinearRecurrence[{3, -3, 1}, {70, 44, 468}, 40] (* Vincenzo Librandi, Feb 02 2012 *)

Prog

(PARI) a(n)=225*n^2-251*n+70 \\ Charles R Greathouse IV, Dec 23 2011
(Magma) I:=[70, 44, 468]; [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 - 251*n + 70 for n in (0..40)] # G. C. Greubel, Jun 10 2021

Crossrefs

Cf. A156840.

Sequence in context: A033390 A129352 A318571 * A252714 A245046 A265727

Adjacent sequences: A156807 A156808 A156809 * A156811 A156812 A156813

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 16 2009, corrected Feb 20 2009

Extensions

Offset corrected by R. J. Mathar, Aug 18 2009

Status

approved