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A267047 Total number of ON (black) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 5, 9, 14, 22, 27, 39, 44, 60, 65, 85, 90, 114, 119, 147, 152, 184, 189, 225, 230, 270, 275, 319, 324, 372, 377, 429, 434, 490, 495, 555, 560, 624, 629, 697, 702, 774, 779, 855, 860, 940, 945, 1029, 1034, 1122, 1127, 1219, 1224, 1320, 1325, 1425, 1430 (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 10 2016 and Apr 19 2019: (Start)

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>6.

G.f.: (1+2*x+2*x^4+2*x^5-3*x^6) / ((1-x)^3*(1+x)^2).

(End)

MATHEMATICA

rule=91; 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. A267015.

Sequence in context: A215369 A053618 A268345 * A032801 A033818 A320598

Adjacent sequences:  A267044 A267045 A267046 * A267048 A267049 A267050

KEYWORD

nonn,easy,changed

AUTHOR

Robert Price, Jan 09 2016

STATUS

approved

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Last modified April 22 06:35 EDT 2019. Contains 322329 sequences. (Running on oeis4.)