A157376 a(n) = 6561*n^2 - 7732*n + 2278.

1107, 13058, 38131, 76326, 127643, 192082, 269643, 360326, 464131, 581058, 711107, 854278, 1010571, 1179986, 1362523, 1558182, 1766963, 1988866, 2223891, 2472038, 2733307, 3007698, 3295211, 3595846, 3909603, 4236482, 4576483

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 - a(n)*A157377(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 (3,-3,1).

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(-1107-9737*x-2278*x^2)/(x-1)^3.

E.g.f.: (6561*x^2 - 1171*x + 2278)*exp(x) - 2278. - G. C. Greubel, Feb 04 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {1107, 13058, 38131}, 40]
Table[6561*n^2-7732*n+2278, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)

Prog

(Magma) I:=[1107, 13058, 38131]; [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) = 6561*n^2 - 7732*n + 2278.

Crossrefs

Cf. A157377, A157378.

Sequence in context: A180296 A252552 A295991 * A185501 A322535 A184370

Adjacent sequences: A157373 A157374 A157375 * A157377 A157378 A157379

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved