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A158765 a(n) = 76*n^2 - 1. 2
75, 303, 683, 1215, 1899, 2735, 3723, 4863, 6155, 7599, 9195, 10943, 12843, 14895, 17099, 19455, 21963, 24623, 27435, 30399, 33515, 36783, 40203, 43775, 47499, 51375, 55403, 59583, 63915, 68399, 73035, 77823, 82763, 87855, 93099, 98495 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (76*n^2 - 1)^2 - (1444*n^2 - 38)*(2*n)^2 = 1 can be written as a(n)^2 - A158764(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.: x*(-75 - 78*x + x^2)/(x-1)^3.

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

MATHEMATICA

76*Range[40]^2-1 (* or *) LinearRecurrence[{3, -3, 1}, {75, 303, 683}, 40] (* Harvey P. Dale, Jan 18 2012 *)

PROG

(MAGMA) I:=[75, 303, 683]; [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=1, 40, print1(76*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A005843, A158764.

Sequence in context: A174685 A158742 A292313 * A226741 A223078 A055561

Adjacent sequences:  A158762 A158763 A158764 * A158766 A158767 A158768

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 26 2009

EXTENSIONS

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

STATUS

approved

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Last modified September 16 12:41 EDT 2019. Contains 327113 sequences. (Running on oeis4.)