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A263807 Total number of ON (black) cells after n iterations of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell. 2
1, 3, 6, 11, 17, 25, 34, 45, 57, 71, 86, 103, 121, 141, 162, 185, 209, 235, 262, 291, 321, 353, 386, 421, 457, 495, 534, 575, 617, 661, 706, 753, 801, 851, 902, 955, 1009, 1065, 1122, 1181, 1241, 1303, 1366, 1431, 1497, 1565, 1634, 1705, 1777, 1851, 1926 (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

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 20 2016 and Apr 16 2019: (Start)

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

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

(End)

MATHEMATICA

rule=157; 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. A263804.

Sequence in context: A022775 A025743 A022338 * A176708 A273140 A320272

Adjacent sequences: A263804 A263805 A263806 * A263808 A263809 A263810

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified December 4 19:07 EST 2022. Contains 358563 sequences. (Running on oeis4.)