[seqfan] Re: definition of A002848

Alois Heinz heinz at hs-heilbronn.de
Fri Feb 12 00:48:05 CET 2010


Richard Guy schrieb:
> Can we have an example?  Can you partition {1,...,n}
> into triples if  n  is not a multiple of  3 ?
>   
No, but a subset can be partitioned.

A002848(7) = 3:
[1, 3, 4], [2, 5, 7]
[1, 5, 6], [3, 4, 7]
[2, 3, 5], [1, 6, 7]

A002848(8) = 7:
[1, 3, 4], [2, 6, 8]
[1, 4, 5], [2, 6, 8]
[1, 6, 7], [3, 5, 8]
[2, 3, 5], [1, 7, 8]
[2, 4, 6], [1, 7, 8]
[2, 4, 6], [3, 5, 8]
[3, 4, 7], [2, 6, 8]

A002848(10) = 12:
[1, 4, 5], [2, 6, 8], [3, 7, 10]
[1, 4, 5], [3, 6, 9], [2, 8, 10]
[1, 5, 6], [3, 4, 7], [2, 8, 10]
[1, 6, 7], [4, 5, 9], [2, 8, 10]
[1, 7, 8], [2, 3, 5], [4, 6, 10]
[1, 8, 9], [2, 3, 5], [4, 6, 10]
[1, 8, 9], [2, 4, 6], [3, 7, 10]
[1, 8, 9], [2, 5, 7], [4, 6, 10]
[2, 4, 6], [3, 5, 8], [1, 9, 10]
[2, 6, 8], [3, 4, 7], [1, 9, 10]
[2, 6, 8], [4, 5, 9], [3, 7, 10]
[2, 7, 9], [3, 5, 8], [4, 6, 10]

Alois






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