[seqfan] All-Fives Domino Sequence

Ali Sada pemd70 at yahoo.com
Wed Jun 10 23:07:49 CEST 2020


Hi Everyone,

In Iraq, we play a variation of the All-Five game called Aznif. (Some scholars say the name comes of an Armenian word that means “noble lady”). 

These are the rules:

1)    You can start with any tile.
2)    The first double on the ground becomes the (only) spinner.
3)    The goal is to score as many multiples of 5 by adding the numbers on the ends in each step. (The points on the spinner don’t count after it is covered from 2 sides).


In this variation, we can score 470 points using all 28 tiles of the order 6 domino set. These pictures show how, step by step: 

https://justpaste.it/2ipxj

I don't have a proof, but I think we can’t score more than 470.

The sequence here is the total points we can score using a domino set of order n.

For, n = 0, we have only one tile 0—0, and we can’t score anything. So, a(0) = 0.
For, n = 1, we have three tiles, and we can’t score anything. So, a(1) = 0.
For n = 2, we have six tiles. We can only score 5 once. So, a(2) = 5.
For n = 3, we have ten tiles. We can score, 5+5+10+10+10+10. So, a(3) = 50.

And so on.
The question is: can we find a way to count the scores for domino sets with higher orders (other than trial and error)?
Also, is this sequence suitable for the OEIS?

Best,

Ali




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