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A263511 Total number of ON (black) cells after n iterations of the "Rule 155" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 6, 12, 19, 29, 40, 54, 69, 87, 106, 128, 151, 177, 204, 234, 265, 299, 334, 372, 411, 453, 496, 542, 589, 639, 690, 744, 799, 857, 916, 978, 1041, 1107, 1174, 1244, 1315, 1389, 1464, 1542, 1621, 1703, 1786, 1872, 1959, 2049, 2140, 2234, 2329, 2427 (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

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

G.f.: (1+x+2*x^3)/((1-x)^3*(1+x)). - Vincenzo Librandi, Jan 18 2016

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>3. - Vincenzo Librandi, Jan 18 2016

MATHEMATICA

rule=155; 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 *)

LinearRecurrence[{2, 0, -2, 1}, {1, 3, 6, 12}, 50] (* Vincenzo Librandi, Jan 18 2016 *)

PROG

(MAGMA) I:=[1, 3, 6, 12]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..60]]; // Vincenzo Librandi, Jan 18 2016

CROSSREFS

Cf. A263243.

Sequence in context: A318872 A267591 A101423 * A180622 A125851 A209489

Adjacent sequences:  A263508 A263509 A263510 * A263512 A263513 A263514

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified September 23 19:18 EDT 2020. Contains 337315 sequences. (Running on oeis4.)