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A158492 a(n) = 100*n^2 + 10. 2
10, 110, 410, 910, 1610, 2510, 3610, 4910, 6410, 8110, 10010, 12110, 14410, 16910, 19610, 22510, 25610, 28910, 32410, 36110, 40010, 44110, 48410, 52910, 57610, 62510, 67610, 72910, 78410, 84110, 90010, 96110, 102410, 108910, 115610, 122510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (20*n^2 + 1)^2 - (100*n^2 + 10)*(2*n)^2 = 1 can be written as A158493(n)^2 - a(n)*A005843(n)^2 = 1. - Vincenzo Librandi, Feb 21 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

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

FORMULA

From Vincenzo Librandi, Feb 21 2012: (Start)

G.f.: -(10 + 80*x + 110*x^2)/(x-1)^3;

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {10, 110, 410}, 50] (* Vincenzo Librandi, Feb 21 2012

100Range[0, 40]^2+10 (* Harvey P. Dale, Dec 30 2019 *)

PROG

(MAGMA) I:=[10, 110, 410]; [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, Feb 21 2012

(PARI) for(n=0, 40, print1(100*n^2 + 10", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A005843, A158493.

Sequence in context: A097257 A043996 A044723 * A249845 A180290 A110251

Adjacent sequences:  A158489 A158490 A158491 * A158493 A158494 A158495

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Edited by N. J. A. Sloane, Oct 12 2009

STATUS

approved

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Last modified January 18 19:40 EST 2020. Contains 331029 sequences. (Running on oeis4.)