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A158737 1296n^2 - 36. 2
1260, 5148, 11628, 20700, 32364, 46620, 63468, 82908, 104940, 129564, 156780, 186588, 218988, 253980, 291564, 331740, 374508, 419868, 467820, 518364, 571500, 627228, 685548, 746460, 809964, 876060, 944748, 1016028, 1089900, 1166364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (72*n^2-1)^2-(1296*n^2-36)*(2*n)^2 = 1 can be written as A158738(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 to sequences with linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: 36*x*(-35-38*x+x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1260, 5148, 11628}, 50] (* Vincenzo Librandi, Feb 20 2012 *)

PROG

(MAGMA) I:=[1260, 5148, 11628]; [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 20 2012

(PARI) for(n=1, 40, print1(1296*n^2 - 36", ")); \\ Vincenzo Librandi, Feb 20 2012

CROSSREFS

Cf. A005843, A158738.

Sequence in context: A144563 A175746 A179690 * A203402 A047634 A172314

Adjacent sequences:  A158734 A158735 A158736 * A158738 A158739 A158740

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 25 2009

EXTENSIONS

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

STATUS

approved

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Last modified November 22 08:48 EST 2014. Contains 249805 sequences.