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A158319 441n - 1. 3
440, 881, 1322, 1763, 2204, 2645, 3086, 3527, 3968, 4409, 4850, 5291, 5732, 6173, 6614, 7055, 7496, 7937, 8378, 8819, 9260, 9701, 10142, 10583, 11024, 11465, 11906, 12347, 12788, 13229, 13670, 14111, 14552, 14993, 15434, 15875, 16316, 16757 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (441*n-1)^2-(441*n^2-2*n)*(21)^2=1 can be written as a(n)^2-A157737(n)*(21)^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*(21^2*t-2)).

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

FORMULA

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

G.f.: x*(440+x)/(1-x)^2.

MATHEMATICA

LinearRecurrence[{2, -1}, {440, 881}, 50]

441*Range[40]-1 (* Harvey P. Dale, Apr 11 2017 *)

PROG

(MAGMA) I:=[440, 881]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

(PARI) a(n) = 441*n - 1.

CROSSREFS

Cf. A157737.

Sequence in context: A279812 A279950 A072604 * A250879 A247722 A234202

Adjacent sequences:  A158316 A158317 A158318 * A158320 A158321 A158322

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 16 2009

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)