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A158742 a(n) = 74*n^2 + 1. 2
1, 75, 297, 667, 1185, 1851, 2665, 3627, 4737, 5995, 7401, 8955, 10657, 12507, 14505, 16651, 18945, 21387, 23977, 26715, 29601, 32635, 35817, 39147, 42625, 46251, 50025, 53947, 58017, 62235, 66601, 71115, 75777, 80587, 85545, 90651, 95905 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (74*n^2 + 1)^2 - (1369*n^2 + 37)*(2*n)^2 = 1 can be written as a(n)^2 - A158741(n)*A005843(n))^2 = 1.

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

G.f.: -(1 + 72*x + 75*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 75, 297}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PROG

(MAGMA) I:=[1, 75, 297]; [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(74*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A005843, A158741.

Sequence in context: A098230 A258056 A174685 * A292313 A158765 A226741

Adjacent sequences:  A158739 A158740 A158741 * A158743 A158744 A158745

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 25 2009

EXTENSIONS

Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009

STATUS

approved

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Last modified September 20 12:43 EDT 2019. Contains 327238 sequences. (Running on oeis4.)