A267598 - OEIS

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A267598

Triangle read by rows giving successive states of cellular automaton generated by "Rule 177" initiated with a single ON (black) cell.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

COMMENTS

Row n has length 2n+1.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

a(n) = (1 - (-1)^(n + floor(sqrt(n + 2))))/2 (conjecture). - Velin Yanev, Nov 15 2016

EXAMPLE

The first ten rows:

0 0 1

0 1 0 0 1

0 1 0 1 0 0 1

0 1 0 1 0 1 0 0 1

0 1 0 1 0 1 0 1 0 0 1

0 1 0 1 0 1 0 1 0 1 0 0 1

0 1 0 1 0 1 0 1 0 1 0 1 0 0 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1

MATHEMATICA

rule=177; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Flatten[catri] (* Triangle Representation of CA *)

CROSSREFS

Sequence in context: A232990 A285076 A338353 * A194681 A359764 A065043

Adjacent sequences: A267595 A267596 A267597 * A267599 A267600 A267601

KEYWORD

nonn,tabf,easy

AUTHOR

Robert Price, Jan 18 2016

STATUS

approved