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A158543 a(n) = 144*n^2 - 12. 2
132, 564, 1284, 2292, 3588, 5172, 7044, 9204, 11652, 14388, 17412, 20724, 24324, 28212, 32388, 36852, 41604, 46644, 51972, 57588, 63492, 69684, 76164, 82932, 89988, 97332, 104964, 112884, 121092, 129588, 138372, 147444, 156804, 166452 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (24*n^2 - 1)^2 - (144*n^2 - 12)*(2*n)^2 = 1 can be written as A158544(n)^2 - a(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: -x*(132 + 168*x - 12*x^2)/(x-1)^3. - Vincenzo Librandi, Feb 14 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 14 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {132, 564, 1284}, 50] (* Vincenzo Librandi, Feb 14 2012 *)

144*Range[40]^2-12 (* Harvey P. Dale, Oct 20 2012 *)

PROG

(MAGMA) I:=[132, 564, 1284]; [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 14 2012

(PARI) for(n=1, 40, print1(144*n^2 - 12", ")); \\ Vincenzo Librandi, Feb 14 2012

CROSSREFS

Cf. A005843, A158544.

Sequence in context: A204834 A241288 A115132 * A156958 A305271 A090199

Adjacent sequences:  A158540 A158541 A158542 * A158544 A158545 A158546

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Comment rewritten by R. J. Mathar, Oct 16 2009

STATUS

approved

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Last modified August 25 05:06 EDT 2019. Contains 326318 sequences. (Running on oeis4.)