A157377 a(n) = 531441*n - 313146.

218295, 749736, 1281177, 1812618, 2344059, 2875500, 3406941, 3938382, 4469823, 5001264, 5532705, 6064146, 6595587, 7127028, 7658469, 8189910, 8721351, 9252792, 9784233, 10315674, 10847115, 11378556, 11909997, 12441438, 12972879

Offset

1,1

Comments

The identity (43046721*n^2-50729652*n+14945959)^2-(6561*n^2-7732*n+2278)*(531441*n-313146)^2=1 can be written as A157378(n)^2-A157376(n)*a(n)^2=1.

Links

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

Vincenzo Librandi, X^2-AY^2=1

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

Formula

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

G.f.: x*(218295+313146*x)/(x-1)^2.

E.g.f.: 81*((6561*x - 3866)*exp(x) + 3866). - G. C. Greubel, Feb 04 2018

Maple

A157377:=n->531441*n - 313146: seq(A157377(n), n=1..40); # Wesley Ivan Hurt, Jan 19 2017

Mathematica

LinearRecurrence[{2, -1}, {218295, 749736}, 40]
Table[531441*n-313146, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)

Prog

(Magma) I:=[218295, 749736]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 531441*n - 313146.

Crossrefs

Cf. A157376, A157378.

Sequence in context: A205734 A205915 A205907 * A090873 A236040 A251480

Adjacent sequences: A157374 A157375 A157376 * A157378 A157379 A157380

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved