A156812 a(n) = 225*n^2 - 199*n + 44.

44, 70, 546, 1472, 2848, 4674, 6950, 9676, 12852, 16478, 20554, 25080, 30056, 35482, 41358, 47684, 54460, 61686, 69362, 77488, 86064, 95090, 104566, 114492, 124868, 135694, 146970, 158696, 170872, 183498, 196574, 210100, 224076, 238502, 253378

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

Cf. A156813, A156814.

Sequence in context: A092025 A250329 A242515 * A171665 A348098 A348076

Adjacent sequences: A156809 A156810 A156811 * A156813 A156814 A156815

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 16 2009

Extensions

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

Status

approved