# [seqfan] Re: Binary Palindrome Subsequences

Max Alekseyev maxale at gmail.com
Mon Dec 15 20:04:17 CET 2008

```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

On Mon, Dec 15, 2008 at 10:03 AM, Benoît Jubin <benoit.jubin at gmail.com> wrote:
> It seems that you are counting "factors" or "subwords" starting and
> ending with one, rather than subsequences.
> Indeed, 111, 1111 and 11111 are also subsequences, for 203.
>
> Benoit
>
>
> On Mon, Dec 15, 2008 at 9:02 AM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:
>> 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.
>>
>> For most n, it seems, a(n) = A000120(n).
>>
>> (A000120(n) is the number of 1's digits in the binary representation of n.)
>>
>> But there are exceptions.
>>
>> For instance, 203 = 11001011 in binary.
>>
>> A000120(203) = 5, obviously.
>>
>> But I count 4 palindromic subsequences, each ending and starting with 1: 1, 11, 101, 1001.
>>
>> What is the sequence of positive integers n where a(n) does NOT = A000120(n).
>>
>> ....203, 211,...
>>
>> (I guess this sequence starts with 203, but I may have made an error.)
>>
>> Thanks,
>> Leroy Quet
>>
>>
>>
>>
>>
>>
>>
>>
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