[seqfan] Binary Palindrome Subsequences

[Leroy Quet]

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