[seqfan] New interpretation of A001045 - Jacobsthal numbers?

[N. J. A. Sloane]

Dear Seqfans,   This message just arrived. (I do not know the author.)
Can anyone answer it?
Neil


> >From toby at gottfriedville.net Sat Nov  1 20:32:17 2008
> Delivered-To: njas at research.att.com
> From: <toby at gottfriedville.net>
> To: <njas at research.att.com>, <ed at mathpuzzle.com>
> Subject: Cannot find this particular result anywhere (A001045 - Jacobsthal numbers)
> Date: Sat, 1 Nov 2008 17:32:52 -0700
> 
> Someone on Yahoo Answers posed the question
> 
> "How many ways are there to tile a 2 x N rectangle
>     using 1x2 dominoes and 2x2 squares ?"
> 
> The result from a computer program was:
> 1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691
> which is http://www.research.att.com/~njas/sequences/A001045
> the Jacobsthal numbers.
> 
> On that page it says 
>  Number of ways to tile a 3 X (n-1) rectangle with 1 X 1 and 2 X 2 square tiles.
> which is a similar problem.
> 
> Considering the basic nature of this problem
> and the number of other applications of this sequence,
> it would be quite a surprise if this were a new result,
> but after a fairly extensive search on Google, I could
> not find it anywhere.
> 
> Any comments ?

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