A157952 a(n) = 162*n + 1.

163, 325, 487, 649, 811, 973, 1135, 1297, 1459, 1621, 1783, 1945, 2107, 2269, 2431, 2593, 2755, 2917, 3079, 3241, 3403, 3565, 3727, 3889, 4051, 4213, 4375, 4537, 4699, 4861, 5023, 5185, 5347, 5509, 5671, 5833, 5995, 6157, 6319, 6481, 6643, 6805, 6967

Offset: 1

Author

Vincenzo Librandi, Mar 10 2009

Keywords

• nonn
• easy

Comments

The identity (162*n + 1)^2 - (81*n^2 + n)*18^2 = 1 can be written as a(n)^2 - (A017162(n) + n)*18^2 = 1. - Vincenzo Librandi, Feb 10 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• 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 (2, -1).

Crossrefs

Cf. A017162.

Programs

Magma

I:=[163, 325]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012

Mathematica

162Range[50]+1 (* or *) LinearRecurrence[{2,-1},{163,325},50](* Harvey P. Dale, Aug 10 2011 *)

PARI

for(n=1, 50, print1(162*n+1", ")); \\ Vincenzo Librandi, Feb 10 2012

Formula

a(n) = 2*a(n-1) - a(n-2), a(0)=163, a(1)=325. - Harvey P. Dale, Aug 10 2011

G.f.: x*(163-x)/(1-x)^2. - Vincenzo Librandi, Feb 10 2012