A158373 625n^2 - 2n.

623, 2496, 5619, 9992, 15615, 22488, 30611, 39984, 50607, 62480, 75603, 89976, 105599, 122472, 140595, 159968, 180591, 202464, 225587, 249960, 275583, 302456, 330579, 359952, 390575, 422448, 455571, 489944, 525567, 562440, 600563, 639936

Offset

1,1

Comments

The identity (625*n-1)^2-(625*n^2-2*n)*(25)^2=1 can be written as A158374(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*(-623-627*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {623, 2496, 5619}, 50]

Prog

(Magma) I:=[623, 2496, 5619]; [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. A158374.

Sequence in context: A345810 A330932 A255086 * A371666 A265119 A283898

Adjacent sequences: A158370 A158371 A158372 * A158374 A158375 A158376

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved