A156865 a(n) = 729000*n - 612180.

116820, 845820, 1574820, 2303820, 3032820, 3761820, 4490820, 5219820, 5948820, 6677820, 7406820, 8135820, 8864820, 9593820, 10322820, 11051820, 11780820, 12509820, 13238820, 13967820, 14696820, 15425820, 16154820, 16883820

Offset

1,1

Comments

The identity (32805000*n^2 - 55096200*n + 23133601)^2 - (2025*n^2 - 649*n + 52)*(729000*n - 612180)^2 = 1 can be written as A157078(n)^2 - A156853(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*(649+3401*x)/(1-x)^2.

E.g.f.: 180*(3401 - (3401 - 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022

Mathematica

LinearRecurrence[{2, -1}, {116820, 845820}, 40]

Prog

(Magma) I:=[116820, 845820]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(PARI) a(n)=729000*n-612180 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [180*(4050*n - 3401) for n in (1..30)] # G. C. Greubel, Jan 28 2022

Crossrefs

Cf. A156853, A157078.

Sequence in context: A252886 A046407 A156417 * A233681 A246557 A289911

Adjacent sequences: A156862 A156863 A156864 * A156866 A156867 A156868

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Status

approved