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A070909 Triangle read by rows giving successive states of cellular automaton generated by "Rule 28" and by "Rule 156". 13
1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row n has length n+1.

Contribution from Gary W. Adamson, May 15 2010: (Start)

Eigensequence of the triangle = A038754. (i.e. 1, 1, 2, 3, 6, 9, 18,...) shifts

to the left with multiplication by triangle A070909.

Binomial transform of A070909 = triangle A177953. (End)

Contribution from Paul Barry, Nov 03 2010: (Start)

Generalized (conditional) Riordan array with k-th column generated by If(mod(k,2)=0,x^k/(1-x),x^k).

A181651 is an eigentriangle. Inverse is A181650. (End)

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

LINKS

Table of n, a(n) for n=0..98.

Index entries for sequences related to cellular automata

Eric Weisstein's World of Mathematics, Rule 28

EXAMPLE

Contribution from Paul Barry, Nov 03 2010: (Start)

Triangle begins

1,

1, 1,

1, 0, 1,

1, 0, 1, 1,

1, 0, 1, 0, 1,

1, 0, 1, 0, 1, 1,

1, 0, 1, 0, 1, 0, 1,

1, 0, 1, 0, 1, 0, 1, 1,

1, 0, 1, 0, 1, 0, 1, 0, 1,

1, 0, 1, 0, 1, 0, 1, 0, 1, 1,

Production matrix begins

1, 1,

0, -1, 1,

0, -1, 1, 1,

0, 0, 0, -1, 1,

0, 0, 0, -1, 1, 1,

0, 0, 0, 0, 0, -1, 1,

0, 0, 0, 0, 0, -1, 1, 1,

0, 0, 0, 0, 0, 0, 0, -1, 1,

0, 0, 0, 0, 0, 0, 0, -1, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1 (End)

MATHEMATICA

rows = 14; ca = CellularAutomaton[28, {{1}, 0}, rows-1]; Flatten[Table[ca[[k, 1 ;; k]], {k, 1, rows}]] (* Jean-Fran├žois Alcover, May 24 2012 *)

CROSSREFS

Cf. A038754, A070909 [From Gary W. Adamson, May 15 2010]

Sequence in context: A131218 A174391 A113998 * A115954 A115526 A054524

Adjacent sequences:  A070906 A070907 A070908 * A070910 A070911 A070912

KEYWORD

nonn,tabl

AUTHOR

Hans Havermann, May 26 2002

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)