A158562 a(n) = 256*n^2 - 16.

240, 1008, 2288, 4080, 6384, 9200, 12528, 16368, 20720, 25584, 30960, 36848, 43248, 50160, 57584, 65520, 73968, 82928, 92400, 102384, 112880, 123888, 135408, 147440, 159984, 173040, 186608, 200688, 215280, 230384, 246000, 262128, 278768, 295920, 313584, 331760

Offset

1,1

Comments

The identity (32*n^2 - 1)^2 - (256*n^2 - 16)*(2*n)^2 = 1 can be written as A158563(n)^2 - a(n)*A005843(n)^2 = 1. [rewritten by R. J. Mathar, Oct 16 2009]

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.: 16*x*(-15 - 18*x + x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 09 2023: (Start)

Sum_{n>=1} 1/a(n) = (4 - Pi)/128.

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)*Pi - 4)/128. (End)

Mathematica

16(16Range[40]^2-1) (* or *) LinearRecurrence[{3, -3, 1}, {240, 1008, 2288}, 40] (* Harvey P. Dale, Sep 13 2011 *)

Prog

(Magma) I:=[240, 1008, 2288]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2012
(PARI) for(n=1, 50, print1(256*n^2-16", ")); \\ Vincenzo Librandi, Feb 15 2012

Crossrefs

Cf. A005843, A158563.

Sequence in context: A060663 A092000 A124352 * A234728 A234721 A235212

Adjacent sequences: A158559 A158560 A158561 * A158563 A158564 A158565

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Status

approved