This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A071051 Number of 1's in n-th row of triangle in A071035. 4
 1, 3, 4, 7, 4, 8, 8, 15, 4, 8, 8, 16, 8, 16, 16, 31, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 63, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 127, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of ON cells at generation n of 1-D CA defined by Rule 126, starting with a single ON cell. - N. J. A. Sloane, Aug 09 2014 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3. LINKS Robert Price, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015. S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601--644. FORMULA a(2n) = a(n)+A036987(n); a(2n+1) = a(n)+2*2^A000120(n). - Benoit Cloitre, Sep 22 2003 a(n) = 2^(1+wt(n)) unless n is of the form 2^i-1 in which case we must subtract 1, where wt = A000120. - N. J. A. Sloane, Aug 09 2014 G.f.: 2*Prod_{k=0..oo} (1+2*x^(2^k)) - Sum_k=0..oo} x^(2^k-1). - N. J. A. Sloane, Aug 09 2014 EXAMPLE [Contribution from Omar E. Pol, Dec 11 2010] (Start) May be arranged in blocks of sizes 1, 1, 2, 4, 8, 16, 32, ...: 1, 3, 4, 7, 4, 8, 8, 15, 4, 8, 8, 16, 8, 16, 16, 31, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 63, Last terms of rows give positive terms of A000225. (End) MATHEMATICA a[n_] := 2^(DigitCount[n, 2, 1]+1) - Boole[IntegerQ[Log[2, n+1]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2018, from 2nd formula *) CROSSREFS Cf. A001316, A071051, A000120, A036987, A000225. Sequence in context: A193967 A109823 A267447 * A212807 A163830 A254931 Adjacent sequences:  A071048 A071049 A071050 * A071052 A071053 A071054 KEYWORD nonn AUTHOR Hans Havermann, May 26 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 20 12:32 EST 2019. Contains 319330 sequences. (Running on oeis4.)