A157369 a(n) = 343*n - 273.

70, 413, 756, 1099, 1442, 1785, 2128, 2471, 2814, 3157, 3500, 3843, 4186, 4529, 4872, 5215, 5558, 5901, 6244, 6587, 6930, 7273, 7616, 7959, 8302, 8645, 8988, 9331, 9674, 10017, 10360, 10703, 11046, 11389, 11732, 12075, 12418, 12761, 13104, 13447

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-A157368(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

G.f: x*(70+273*x)/(1-x)^2.

E.g.f.: 7*(39 - (39-49*x)*exp(x)). - G. C. Greubel, Feb 02 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {70, 413, 756}, 40]
343Range[40]-273  (* Harvey P. Dale, Mar 13 2011 *)

Prog

(Magma) I:=[70, 413, 756]; [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)= 343*n-273.

Crossrefs

Cf. A157368, A157370.

Sequence in context: A295770 A151556 A172222 * A163434 A154085 A220365

Adjacent sequences: A157366 A157367 A157368 * A157370 A157371 A157372

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved