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

Author

Jack W Grahl, Aug 14 2009

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A164349, A164362, A164364.

Programs

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 *)

Formula

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

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

Extensions

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