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A157509 a(n) = 13122*n^2 - 324*n + 1. 3
12799, 51841, 117127, 208657, 326431, 470449, 640711, 837217, 1059967, 1308961, 1584199, 1885681, 2213407, 2567377, 2947591, 3354049, 3786751, 4245697, 4730887, 5242321, 5779999, 6343921, 6934087, 7550497, 8193151, 8862049 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as a(n)^2 - A157507(n)* A157508(n)^2 = 1. - Vincenzo Librandi, Jan 26 2012

This is the case s=9 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Jan 26 2011

LINKS

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

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(-12799 - 13444*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {12799, 51841, 117127}, 40] (* Vincenzo Librandi, Jan 26 2012 *)

Table[13122n^2-324n+1, {n, 30}] (* Harvey P. Dale, Jun 30 2022 *)

PROG

(Magma) I:=[12799, 51841, 117127]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012

(PARI) for(n=1, 22, print1(13122n^2 - 324n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012

CROSSREFS

Cf. A157507, A157508.

Sequence in context: A206966 A209091 A207133 * A035916 A243050 A246809

Adjacent sequences: A157506 A157507 A157508 * A157510 A157511 A157512

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 02 2009

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)