# [seqfan] Re: Binary Palindrome Subsequences

Max Alekseyev maxale at gmail.com
Mon Dec 15 21:01:33 CET 2008

```There may be ambiguity whether "substring" refers to just a string
appearing as a substring in the given string, or to a string *and its
position* inside the given string.
According to the latter definition, any string of length n contains
exactly n*(n+1)/2 distinct non-empty substrings; while according to
the former definition, the number of distinct substrings depends on
the given string.

Regards,
Max

On Mon, Dec 15, 2008 at 11:39 AM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:
> I meant to say substrings, not subsequences.
>
> I don't want the SUBSTRINGS counted with multiplicity. I hope that is clear enough when I said I was counting the number of "distinct" substrings (or subsequences, whatever they are). Was I clear enough, or does "distinct" have another possible meaning here?
>
> Thanks,
> Leroy Quet
>
>
>
>
> --- On Mon, 12/15/08, Max Alekseyev <maxale at gmail.com> wrote:
>
>> Better say substrings.
>> Another issue is whether they are counted with
>> multiplicities or not.
>> For example, n=3 equal "11" in binary contains
>> the substring "1"  two times.
>>
>> Regards,
>> Max
>>
>
>
> I said:
>
>>>Let a(n) = the number of distinct palindromic subsequences, each subsequence starting and ending with 1, that are contained in the binary representation of n.
>
>
>
>
>
>
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>

```