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A267529 Total number of ON (black) cells after n iterations of the "Rule 141" elementary cellular automaton starting with a single ON (black) cell. 2
1, 2, 4, 7, 12, 18, 26, 35, 46, 58, 72, 87, 104, 122, 142, 163, 186, 210, 236, 263, 292, 322, 354, 387, 422, 458, 496, 535, 576, 618, 662, 707, 754, 802, 852, 903, 956, 1010, 1066, 1123, 1182, 1242, 1304, 1367, 1432, 1498, 1566, 1635, 1706, 1778, 1852, 1927 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apart from initial terms, is this same as A132297 ?

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

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 16 2016 and Apr 20 2019: (Start)

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4.

G.f.: (1+x^3+x^4) / ((1-x)^3*(1+x)).

(End)

MATHEMATICA

rule=141; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

CROSSREFS

Cf. A267525.

Sequence in context: A084672 A011910 A227590 * A005521 A135901 A124197

Adjacent sequences:  A267526 A267527 A267528 * A267530 A267531 A267532

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 16 2016

STATUS

approved

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Last modified September 17 16:50 EDT 2021. Contains 347487 sequences. (Running on oeis4.)