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A157956 a(n) = 200*n + 1. 3
201, 401, 601, 801, 1001, 1201, 1401, 1601, 1801, 2001, 2201, 2401, 2601, 2801, 3001, 3201, 3401, 3601, 3801, 4001, 4201, 4401, 4601, 4801, 5001, 5201, 5401, 5601, 5801, 6001, 6201, 6401, 6601, 6801, 7001, 7201, 7401, 7601, 7801, 8001, 8201, 8401, 8601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (200*n + 1)^2 - (100*n^2 + n)*20^2 = 1 can be written as a(n)^2 - A055438(n)*20^2 = 1. - Vincenzo Librandi, Feb 04 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 14 in the first table at p. 85, case d(t) = t*(10^2*t+1)).

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

FORMULA

G.f.: x*(201-x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012

MATHEMATICA

200Range[50]+1  (* Harvey P. Dale, Feb 24 2011 *)

LinearRecurrence[{2, -1}, {201, 401}, 50] (* Vincenzo Librandi, Feb 04 2012 *)

PROG

MAGMA) I:=[201, 401]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012

(PARI) for(n=1, 50, print1(200*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012

CROSSREFS

Cf. A055438.

Sequence in context: A338591 A259768 A076192 * A202771 A183350 A226566

Adjacent sequences:  A157953 A157954 A157955 * A157957 A157958 A157959

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 10 2009

STATUS

approved

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Last modified June 20 23:44 EDT 2021. Contains 345316 sequences. (Running on oeis4.)