A156854 a(n) = 2025*n^2 - 3401*n + 1428.

52, 2726, 9450, 20224, 35048, 53922, 76846, 103820, 134844, 169918, 209042, 252216, 299440, 350714, 406038, 465412, 528836, 596310, 667834, 743408, 823032, 906706, 994430, 1086204, 1182028, 1281902, 1385826, 1493800, 1605824, 1721898

Offset

1,1

Comments

The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as A157079(n)^2 - a(n)*A156866(n)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..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).

G.f.: x*(52 +2570*x +1428*x^2)/(1-x)^3.

E.g.f.: -1428 + (1428 - 1376*x + 2025*x^2)*exp(x). - G. C. Greubel, Jan 28 2022

Mathematica

LinearRecurrence[{3, -3, 1}, {52, 2726, 9450}, 40]

Prog

(Magma) I:=[52, 2726, 9450]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=2025*n^2-3401*n+1428 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [(81*n -68)*(25*n -21) for n in (1..40)] # G. C. Greubel, Jan 28 2022

Crossrefs

Cf. A156853, A156866, A157079.

Sequence in context: A189776 A189158 A042301 * A282590 A360444 A027550

Adjacent sequences: A156851 A156852 A156853 * A156855 A156856 A156857

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Status

approved