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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

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), 601--644.

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^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-Fran├žois 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

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