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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Paul Tek, Table of n, a(n) for n = 1..3323

Paul Tek, PERL program for this sequence

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

Cf. A164349, A164363, A164364.

Sequence in context: A052956 A298118 A008930 * A026742 A316471 A018268

Adjacent sequences:  A164359 A164360 A164361 * A164363 A164364 A164365

KEYWORD

nonn

AUTHOR

Jack W Grahl, Aug 14 2009

EXTENSIONS

a(23)-a(26) from Robert G. Wilson v, Aug 17 2009

STATUS

approved

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)