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These are binary sequences (sequences of 1's and 0's), and two sequences are considered the same if one can be transformed into the other by translation and/or exchanging 1 and 0. A periodic sequence can be represented by enclosing one period in parentheses (for example , (00011011)). Even sequences contain an even number of 1's and an even number of 0's. - Michael B. Porter, Dec 22 2019
More terms from _Randall L. Rathbun, _, Jan 11 2002
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For n=2, the sequences of length 2n=4 are (0000), (0001), (0011), and (0101). The other 12 possibilities are equivalent - for example, the sequence (1001) is a translation of (0011), and the sequence (1101) is equivalent to (0001) by exchanging 1's and 0's and then translating. Three Since three of these have an even number of 1's, so a(2) = 3. - Michael B. Porter, Dec 22 2019
These are binary sequences (sequences of 1's and 0's), and two sequences are considered the same if one can be transformed into the other by translation and/or exchanging 1 and 0. A periodic sequence can be represented by enclosing one period in parentheses (for example (00011011)). Even sequences contain an even number of 1's and an even number of 0's. - Michael B. Porter, Dec 22 2019
For n=2, the sequences of length 2n=4 are (0000), (0001), (0011), and (0101). The other 12 possibilities are equivalent - for example, the sequence (1001) is a translation of (0011), and the sequence (1101) is equivalent to (0001) by exchanging 1's and 0's and then translating. Three of these have an even number of 1's, so a(2) = 3. - Michael B. Porter, Dec 22 2019
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