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A164363
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The number of 1's in the n-th stage of A164349
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3
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1, 1, 2, 3, 6, 12, 23, 46, 91, 182, 364, 727, 1454, 2908, 5816, 11631, 23262, 46523, 93046, 186092, 372183, 744366, 1488732, 2977463, 5954926, 11909851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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, A164363 + A164362 = 2**n + 1
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FORMULA
| A recurrence is given in terms of A164364(n) = A164349(2**n)
a(n+1) = 2*a(n) - A164364(n)
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EXAMPLE
| 01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
So the numnber of 1's in the n-th stage is the sequence 1, 1, 2, 3, 6 etc.
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MATHEMATICA
| t = Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 25]; Table[ Count[ Take[t, 2^n + 1], 1], {n, 0, 25}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2009]
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CROSSREFS
| A164349, A164362, A164364
Sequence in context: A019138 A154324 A001630 * A103341 A023675 A029996
Adjacent sequences: A164360 A164361 A164362 * A164364 A164365 A164366
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KEYWORD
| more,nonn
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AUTHOR
| Jack Grahl (jgrahl(AT)math.ucl.ac.uk), Aug 14 2009
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EXTENSIONS
| a(23)- a(26) from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 17 2009
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