A156868 a(n) = 729000*n + 180.

729180, 1458180, 2187180, 2916180, 3645180, 4374180, 5103180, 5832180, 6561180, 7290180, 8019180, 8748180, 9477180, 10206180, 10935180, 11664180, 12393180, 13122180, 13851180, 14580180, 15309180, 16038180, 16767180, 17496180

Offset

1,1

Comments

The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as A157081(n)^2 - A156856(n)*a(n)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2).

G.f.: 180*x*(4051-x)/(1-x)^2.

E.g.f.: 180*(-1 + (1 + 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022

Mathematica

LinearRecurrence[{2, -1}, {729180, 1458180}, 40]
729000*Range[30]+180 (* Harvey P. Dale, Jan 11 2014 *)

Prog

(Magma) I:=[729180, 1458180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];
(PARI) a(n)=729000*n+180 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [180*(4050*n + 1) for n in (1..40)] # G. C. Greubel, Jan 28 2022

Crossrefs

Cf. A156856, A156867, A157081.

Sequence in context: A321495 A234495 A156867 * A238297 A329225 A236901

Adjacent sequences: A156865 A156866 A156867 * A156869 A156870 A156871

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Status

approved