Re: N-Block Tetris Shapes
- From: Robby Goetschalckx <robby@xxxxxxxxxxxxxx>
- Date: Mon, 09 Jan 2006 09:41:59 +0100
yaoziyuan@xxxxxxxxx wrote:
> When I was in elementary school I asked myself: Is there a formula F(n)
> for calculating the number of different n-block Tetris shapes? At that
> time I manually enumerated F(1) to F(6): 1, 1, 2, 7, 18, 1??. (The
> manuscript got lost and I can't recall the exact result for F(6)).
>
> Later I saw a computer program that automatically counted F(n) and
> optionally printed every different n-block shape on screen. It was a
> moderately optimized complete search algorithm.
>
> Now I want to ask whether there is an existing least time-consuming
> algorithm for getting F(n)? Or is it in theory possible to design such
> an algorithm?
http://www.research.att.com/~njas/sequences/A000988
http://mathworld.wolfram.com/Polyomino.html
"The best currently known bounds on the number of n-polyominoes are
3.72^n<P(n)<4.65^n"
.
- References:
- N-Block Tetris Shapes
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- N-Block Tetris Shapes
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