A158369 576n^2 + 2n.

578, 2308, 5190, 9224, 14410, 20748, 28238, 36880, 46674, 57620, 69718, 82968, 97370, 112924, 129630, 147488, 166498, 186660, 207974, 230440, 254058, 278828, 304750, 331824, 360050, 389428, 419958, 451640, 484474, 518460, 553598, 589888

Offset

1,1

Comments

The identity (576*n+1)^2-(576*n^2+2*n)*(24)^2=1 can be written as A158370(n)^2-a(n)*(24)^2=1.

Links

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

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(24^2*t+2)).

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*(578+574*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {578, 2308, 5190}, 50]

Prog

(Magma) I:=[578, 2308, 5190]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 576*n^2 + 2*n.

Crossrefs

Cf. A158370.

Sequence in context: A234500 A252384 A252385 * A366067 A232888 A035754

Adjacent sequences: A158366 A158367 A158368 * A158370 A158371 A158372

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved