A157368 a(n) = 49*n^2 - 78*n + 31.

2, 71, 238, 503, 866, 1327, 1886, 2543, 3298, 4151, 5102, 6151, 7298, 8543, 9886, 11327, 12866, 14503, 16238, 18071, 20002, 22031, 24158, 26383, 28706, 31127, 33646, 36263, 38978, 41791, 44702, 47711, 50818, 54023, 57326, 60727, 64226

Offset

1,1

Comments

The identity (2401*n^2-3822*n+1520)^2-(49*n^2-78*n+31)*( 343*n-273)^2=1 can be written as A157370(n)^2-a(n)*A157369(n)^2=1.

The continued fraction expansion of sqrt(a(n)) is [7n-6; {2, 2, 1, 7n-7, 1, 2, 2, 14n-12}]. For n=1, this collapses to [1; {2}]. - Magus K. Chu, Sep 06 2022

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*(-2-65*x-31*x^2)/(x-1)^3.

E.g.f.: (31 - 29*x + 49*x^2)*exp(x) - 31. - G. C. Greubel, Feb 02 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {2, 71, 238}, 40]

Prog

(Magma) I:=[2, 71, 238]; [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) = 49*n^2 - 78*n + 31.

Crossrefs

Cf. A157369, A157370.

Sequence in context: A164554 A141908 A234298 * A095935 A202813 A081368

Adjacent sequences: A157365 A157366 A157367 * A157369 A157370 A157371

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved