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A158544 a(n) = 24*n^2 - 1. 2
23, 95, 215, 383, 599, 863, 1175, 1535, 1943, 2399, 2903, 3455, 4055, 4703, 5399, 6143, 6935, 7775, 8663, 9599, 10583, 11615, 12695, 13823, 14999, 16223, 17495, 18815, 20183, 21599, 23063, 24575, 26135, 27743, 29399, 31103, 32855, 34655 (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 a(n)^2 - A158543(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*(23 + 26*x - 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}, {23, 95, 215}, 50] (* Vincenzo Librandi, Feb 14 2012 *)

PROG

(MAGMA) I:=[23, 95, 215]; [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(24*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 14 2012

CROSSREFS

Cf. A005843, A158543.

Sequence in context: A042032 A257976 A183011 * A154376 A155815 A231453

Adjacent sequences:  A158541 A158542 A158543 * A158545 A158546 A158547

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 July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)