A158226 a(n) = 225*n^2 - 2*n.

223, 896, 2019, 3592, 5615, 8088, 11011, 14384, 18207, 22480, 27203, 32376, 37999, 44072, 50595, 57568, 64991, 72864, 81187, 89960, 99183, 108856, 118979, 129552, 140575, 152048, 163971, 176344, 189167, 202440, 216163, 230336, 244959, 260032

Offset

1,1

Comments

The identity (225*n-1)^2-(225*n^2-2*n)*(15)^2=1 can be written as A158227(n)^2-a(n)*(15)^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*(15^2*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*(-223-227*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {223, 896, 2019}, 50]
Table[225n^2-2n, {n, 40}] (* Harvey P. Dale, Feb 25 2021 *)

Prog

(Magma) I:=[223, 896, 2019]; [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) = 225*n^2 - 2*n

Crossrefs

Cf. A158227.

Sequence in context: A345198 A094459 A108819 * A253953 A205273 A205266

Adjacent sequences: A158223 A158224 A158225 * A158227 A158228 A158229

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved