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A158679 a(n) = 961*n^2 - 31. 2
930, 3813, 8618, 15345, 23994, 34565, 47058, 61473, 77810, 96069, 116250, 138353, 162378, 188325, 216194, 245985, 277698, 311333, 346890, 384369, 423770, 465093, 508338, 553505, 600594, 649605, 700538, 753393, 808170, 864869, 923490, 984033 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (62*n^2 - 1)^2 - (961*n^2 - 31)*(2*n)^2 = 1 can be written as A158680(n)^2 - a(n)*A005843(n)^2 = 1.

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

G.f.: 31*x*(-30 - 33*x + x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {930, 3813, 8618}, 50] (* Vincenzo Librandi, Feb 19 2012 *)

PROG

(Magma) I:=[930, 3813, 8618]; [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 19 2012

(PARI) for(n=1, 40, print1(961*n^2 - 31", ")); \\ Vincenzo Librandi, Feb 19 2012

CROSSREFS

Cf. A005843, A158680.

Sequence in context: A068651 A175726 A115958 * A250384 A209810 A035856

Adjacent sequences: A158676 A158677 A158678 * A158680 A158681 A158682

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 24 2009

EXTENSIONS

Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009

STATUS

approved

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