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A158123 a(n) = 81*n + 1. 2
82, 163, 244, 325, 406, 487, 568, 649, 730, 811, 892, 973, 1054, 1135, 1216, 1297, 1378, 1459, 1540, 1621, 1702, 1783, 1864, 1945, 2026, 2107, 2188, 2269, 2350, 2431, 2512, 2593, 2674, 2755, 2836, 2917, 2998, 3079, 3160, 3241, 3322, 3403, 3484, 3565 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (81*n + 1)^2 - (81*n^2 + 2*n)*9^2 = 1 can be written as a(n)^2 - A177099(n)*9^2 = 1. - Vincenzo Librandi, Feb 03 2012

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*(9^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

G.f.: x*(82-x)/(1-x)^2. - Vincenzo Librandi, Feb 03 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 03 2012

MATHEMATICA

LinearRecurrence[{2, -1}, {82, 163}, 50] (* Vincenzo Librandi, Feb 03 2012 *)

PROG

(MAGMA) I:=[82, 163]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 03 2012

(PARI) for(n=1, 50, print1(81*n + 1", ")); \\ Vincenzo Librandi, Feb 03 2012

CROSSREFS

Cf. A177099.

Sequence in context: A264352 A044252 A044633 * A044414 A044795 A092229

Adjacent sequences:  A158120 A158121 A158122 * A158124 A158125 A158126

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 13 2009

STATUS

approved

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Last modified August 7 11:38 EDT 2022. Contains 355985 sequences. (Running on oeis4.)