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A164362
The number of 0's in the n-th stage of A164349.
3
1, 2, 3, 6, 11, 21, 42, 83, 166, 331, 661, 1322, 2643, 5285, 10569, 21138, 42275, 84550, 169099, 338197, 676394, 1352787, 2705573, 5411146, 10822291, 21644582, 43289163, 86578325, 173156650, 346313299, 692626597, 1385253193, 2770506386, 5541012771, 11082025542
OFFSET
1,2
COMMENTS
A164349 is generated as follows. Start with the string 01, and at each stage copy the previous string twice and remove the last symbol.
Since the number of symbols in the whole string is 2^n + 1, A164362 + A164363 = 2^n + 1.
FORMULA
A recurrence is given in terms of A164364(n) = A164349(2^n).
a(n+1) = 2*a(n) + A164364(n) - 1.
EXAMPLE
01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
So the number of 0's in the n-th stage is the sequence 1, 2, 3, 6, 11 etc.
MATHEMATICA
t = Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 25]; Table[ Count[ Take[t, 2^n + 1], 0], {n, 0, 25}] (* Robert G. Wilson v, Aug 17 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jack W Grahl, Aug 14 2009
EXTENSIONS
a(23)-a(26) from Robert G. Wilson v, Aug 17 2009
STATUS
approved