[seqfan] Re: definition of A002848

[Richard Guy]

Many thanks.  Neil, could such an example be
included in A002848?   Best,  R.

On Fri, 12 Feb 2010, Alois Heinz wrote:

> 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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