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A158739 1296*n^2 + 36. 2
36, 1332, 5220, 11700, 20772, 32436, 46692, 63540, 82980, 105012, 129636, 156852, 186660, 219060, 254052, 291636, 331812, 374580, 419940, 467892, 518436, 571572, 627300, 685620, 746532, 810036, 876132, 944820, 1016100, 1089972, 1166436 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The identity (72*n^2+1)^2-(1296*n^2+36)*(2*n)^2 = 1 can be written as A158740(n)^2-a(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.: -36*(1+34*x+37*x^2)/(x-1)^3.

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

MAPLE

A158739:=n->1296*n^2+36: seq(A158739(n), n=0..40); # Wesley Ivan Hurt, Nov 20 2014

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {36, 1332, 5220}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PROG

(MAGMA) I:=[36, 1332, 5220]; [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(1296*n^2 + 36", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A005843, A158740.

Sequence in context: A283729 A203333 A226772 * A218518 A099366 A095657

Adjacent sequences:  A158736 A158737 A158738 * A158740 A158741 A158742

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 January 26 06:32 EST 2021. Contains 340434 sequences. (Running on oeis4.)