A158382 a(n) = 625*n^2 + 2*n.

627, 2504, 5631, 10008, 15635, 22512, 30639, 40016, 50643, 62520, 75647, 90024, 105651, 122528, 140655, 160032, 180659, 202536, 225663, 250040, 275667, 302544, 330671, 360048, 390675, 422552, 455679, 490056, 525683, 562560, 600687, 640064

Offset

1,1

Comments

The identity (625*n+1)^2 - (625*n^2+2*n)*(25)^2 = 1 can be written as A158383(n)^2 - a(n)*(25)^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*(25^2*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*(-627-623*x)/(x-1)^3. [corrected by Georg Fischer, May 11 2019]

Mathematica

LinearRecurrence[{3, -3, 1}, {627, 2504, 5631}, 50]

Prog

(Magma) I:=[627, 2504, 5631]; [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) = 625*n^2 + 2*n.

Crossrefs

Cf. A158383.

Sequence in context: A345777 A129974 A031703 * A188362 A098260 A224603

Adjacent sequences: A158379 A158380 A158381 * A158383 A158384 A158385

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved