# [seqfan] Re: Slight error in [Koshy, 2001], corrected in OEIS but not mentioned

Richard Mathar mathar at strw.leidenuniv.nl
Wed Sep 8 14:51:47 CEST 2010

```http://list.seqfan.eu/pipermail/seqfan/2010-September/005997.html :

> Don't know if this matters at all, but in Thomas Koshy's book on Fibonacci
> and Lucas numbers, the formula for even-indexed Lucas numbers in terms of
> squares of Lucas numbers (A001254) is erroneously given as L(2n) = 2L(n)^2 +
> 2(-1)^(n - 1) on page 404 as Identity 34.7. Just a little bit later on the

We might turn this into an advantage and create a new sequence of the following
format:

%I A000001
%N A000001 2*( Lucas(n)^2-(-1)^n) ).
%S A000001 6,4,16,34,96,244,646,1684,4416,11554,30256,79204,207366,542884,1421296,
%T A000001 3720994,9741696,25504084,66770566,174807604,457652256
%H A000001 <a href="Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F A000001 a(n) = 2* (A000032(n))^2 -2*(-1)^n = 2*A047946(n) = 2*a(n-1) +2*a(n-2) -a(n-3).
%F A000001 G.f.: 2*(3-4*x-2*x^2)/( (1+x)*(x^2-3*x+1) ).
%Y A000001 Cf. A001254.
%K A000001 nonn,easy
%O A000001 0,1
%A A000001 Thomas Koshy

```