NEW SEQ?

[Paul D. Hanna]

Zak (and Seqfans), 
     Correction: your sequence is not a table as I thought at first; so
... 
A052937 seems to describe the number of terms in each generation, and  
A024537 seems to describe the sum of the terms in each generation. 
 
And, apart from initial terms, it appears to be already in the OEIS as:  
A104521  Fixed point of the morphism 0->{1}, 1->{1,0,1}. 
 
but I am not sure of these guesses without further checking. 
    Paul   
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