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A158404 841n + 1. 2
842, 1683, 2524, 3365, 4206, 5047, 5888, 6729, 7570, 8411, 9252, 10093, 10934, 11775, 12616, 13457, 14298, 15139, 15980, 16821, 17662, 18503, 19344, 20185, 21026, 21867, 22708, 23549, 24390, 25231, 26072, 26913, 27754, 28595, 29436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (841*n+1)^2-(841*n^2+2*n)*(29)^2=1 can be written as a(n)^2-A158403(n)*(29)^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*(29^2*t+2)).

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

FORMULA

G.f.: x*(842-x)/(1-x)^2.

a(n) = 2*a(n-1)-a(n-2).

MATHEMATICA

LinearRecurrence[{2, -1}, {842, 1683}, 50]

NestList[#+841&, 842, 40] (* Harvey P. Dale, Dec 14 2012 *)

PROG

(MAGMA) I:=[842, 1683]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

(PARI) a(n) = 841*n + 1.

CROSSREFS

Cf. A158403.

Sequence in context: A121499 A253514 A049530 * A004929 A031736 A154473

Adjacent sequences:  A158401 A158402 A158403 * A158405 A158406 A158407

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 18 2009

STATUS

approved

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Last modified July 7 14:34 EDT 2020. Contains 335495 sequences. (Running on oeis4.)