A164363 The number of 1's in the n-th stage of A164349

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, 23819702, 47639404, 95278807, 190557614, 381115228, 762230456, 1524460911, 3048921822, 6097843643

Offset

1,3

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.

Links

Paul Tek, Table of n, a(n) for n = 1..3324

Formula

A recurrence is given in terms of A164364(n) = A164349(2^n):

a(n+1) = 2*a(n) - A164364(n).

Example

01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
So the number of 1's in the n-th stage is the sequence 1, 1, 2, 3, 6 etc.

Mathematica

t = Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 25]; Table[ Count[ Take[t, 2^n + 1], 1], {n, 0, 25}] (* Robert G. Wilson v, Aug 17 2009 *)

Crossrefs

Cf. A164349, A164362, A164364.

Sequence in context: A001630 A293363 A326021 * A306809 A103341 A023675

Adjacent sequences: A164360 A164361 A164362 * A164364 A164365 A164366

Keyword

nonn

Author

Jack W Grahl, Aug 14 2009

Extensions

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

Status

approved