cp's OEIS Frontend

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

%I A164363 #19 Jun 02 2025 01:49:51
%S A164363 1,1,2,3,6,12,23,46,91,182,364,727,1454,2908,5816,11631,23262,46523,
%T A164363 93046,186092,372183,744366,1488732,2977463,5954926,11909851,23819702,
%U A164363 47639404,95278807,190557614,381115228,762230456,1524460911,3048921822,6097843643
%N A164363 The number of 1's in the n-th stage of A164349.
%C A164363 A164349 is generated as follows. Start with the string 01, and at each stage copy the previous string twice and remove the last symbol.
%C A164363 Since the number of symbols in the whole string is 2^n + 1, A164363 + A164362 = 2^n + 1.
%H A164363 Paul Tek, <a href="/A164363/b164363.txt">Table of n, a(n) for n = 1..3324</a>
%F A164363 A recurrence is given in terms of A164364(n) = A164349(2^n):
%F A164363 a(n+1) = 2*a(n) - A164364(n).
%e A164363 01 -> 010 -> 01001 -> 010010100 -> 01001010001001010 etc.
%e A164363 So the number of 1's in the n-th stage is the sequence 1, 1, 2, 3, 6 etc.
%t A164363 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 *)
%Y A164363 Cf. A164349, A164362, A164364.
%K A164363 nonn
%O A164363 1,3
%A A164363 _Jack W Grahl_, Aug 14 2009
%E A164363 a(23)-a(26) from _Robert G. Wilson v_, Aug 17 2009