[seqfan] Re: Slight error in [Koshy, 2001], corrected in OEIS but not mentioned
Alonso Del Arte
alonso.delarte at gmail.com
Wed Sep 8 23:05:08 CEST 2010
I suppose someone might look up that sequence after reading the book and
wondering if anyone else had caught that mistake (actually, I did do that,
yesterday). Today it's in the table as A171089, and it does have my comment
on the typo.
As it turns out, my being engrossed in the Lucas multiplication table is not
as much of a sidetrack from my promise to calculate a b-file for a sequence
pertaining to "phi-nary" numbers: those Lucas numbers that are 2 off from
the square of a smaller Lucas number are precisely the ones that are the sum
of exactly two powers of phi. A comment in A005248 confirmed my hunch.
Al
On Wed, Sep 8, 2010 at 8:51 AM, Richard Mathar <mathar at strw.leidenuniv.nl>wrote:
>
> 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
>
>
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