A157953 a(n) = 81n^2 - n.

80, 322, 726, 1292, 2020, 2910, 3962, 5176, 6552, 8090, 9790, 11652, 13676, 15862, 18210, 20720, 23392, 26226, 29222, 32380, 35700, 39182, 42826, 46632, 50600, 54730, 59022, 63476, 68092, 72870, 77810, 82912, 88176, 93602, 99190, 104940

Offset

1,1

Comments

The identity (162*n - 1)^2 - (81*n^2 - n)*18^2 = 1 can be written as A157954(n)^2 - a(n)*18^2 = 1. - Vincenzo Librandi, Jan 29 2012 [corrected by Jon E. Schoenfield, Aug 18 2018]

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 14 in the first table at p. 85, case d(t) = t*(9^2*t-1)).

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). - Vincenzo Librandi, Jan 29 2012

G.f.: x*(-80-82*x)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {80, 322, 726}, 50] (* Vincenzo Librandi, Jan 29 2012 *)

Prog

(Magma) I:=[80, 322, 726]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(81*n^2 - n", ")); \\ Vincenzo Librandi, Jan 29 2012

Crossrefs

Cf. A157954.

Sequence in context: A057441 A204483 A204475 * A233958 A233951 A045666

Adjacent sequences: A157950 A157951 A157952 * A157954 A157955 A157956

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved