The On-Line Encyclopedia of Integer Sequences (OEIS)

A157913 revision #17

A157913

a(n) = 64*n^2 - 16.

48, 240, 560, 1008, 1584, 2288, 3120, 4080, 5168, 6384, 7728, 9200, 10800, 12528, 14384, 16368, 18480, 20720, 23088, 25584, 28208, 30960, 33840, 36848, 39984, 43248, 46640, 50160, 53808, 57584, 61488, 65520, 69680, 73968, 78384, 82928

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OFFSET

1,1

COMMENTS

The identity (8*n^2 - 1)^2 - (64*n^2 - 16)*n^2 = 1 can be written as A157914(n)^2 - a(n)*n^2 = 1. - Vincenzo Librandi, Feb 09 2012

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*(3 + 6*x - x^2)/(x - 1)^3. - Vincenzo Librandi, Feb 09 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 09 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {48, 240, 560}, 50] (* Vincenzo Librandi, Feb 09 2012 *)

64*Range[40]^2-16 (* Harvey P. Dale, Jul 27 2012 *)

PROG

(MAGMA) I:=[48, 240, 560]; [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 09 2012

(PARI) for(n=1, 40, print1(64*n^2 - 16", ")); \\ Vincenzo Librandi, Feb 09 2012

CROSSREFS

Cf. A157914.

Sequence in context: A211760 A333670 A230136 * * A181773 A052683

Adjacent sequences: A157910 A157911 A157912 * A157914 A157915 A157916

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 09 2009

STATUS

editing