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A267926 Decimal representation of the n-th iteration of the "Rule 246" elementary cellular automaton starting with a single ON (black) cell. 1
1, 7, 23, 119, 375, 1911, 6007, 30583, 96119, 489335, 1537911, 7829367, 24606583, 125269879, 393705335, 2004318071, 6299285367, 32069089143, 100788565879, 513105426295, 1612617054071, 8209686820727, 25801872865143, 131354989131639, 412829965842295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

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..., Fig. 16

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

Conjectures from Colin Barker, Jan 23 2016 and Apr 20 2019: (Start)

a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>2.

G.f.: (1+6*x) / ((1-x)*(1-4*x)*(1+4*x)).

(End)

Empirical a(n) = (25*4^n-3*(-4)^n-7)/15. - Colin Barker, Nov 25 2016 and Apr 20 2019

MATHEMATICA

rule=246; 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 *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

CROSSREFS

Cf. A071041.

Sequence in context: A154113 A053706 A137367 * A228698 A064640 A064639

Adjacent sequences:  A267923 A267924 A267925 * A267927 A267928 A267929

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 22 2016

STATUS

approved

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Last modified August 23 14:26 EDT 2019. Contains 326247 sequences. (Running on oeis4.)