

A071051


Number of 1's in nth 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
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OFFSET

0,2


COMMENTS

Number of ON cells at generation n of 1D 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
A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata...
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), 601644.
Index entries for sequences related to cellular automata


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^i1 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^k1).  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}] (* JeanFrançois 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



