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A267048 Number of OFF (white) cells in the n-th iteration of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell. 1
0, 1, 3, 3, 4, 3, 8, 3, 12, 3, 16, 3, 20, 3, 24, 3, 28, 3, 32, 3, 36, 3, 40, 3, 44, 3, 48, 3, 52, 3, 56, 3, 60, 3, 64, 3, 68, 3, 72, 3, 76, 3, 80, 3, 84, 3, 88, 3, 92, 3, 96, 3, 100, 3, 104, 3, 108, 3, 112, 3, 116, 3, 120, 3, 124, 3, 128, 3, 132, 3, 136, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 (0,2,0,-1).

FORMULA

From Colin Barker, Jan 11 2016: (Start)

a(n) = (2*(-1)^n*n+2*n-7*(-1)^n-1)/2 for n>2.

a(n) = 2*a(n-2)-a(n-4) for n>6.

G.f.: x*(1+3*x+x^2-2*x^3-2*x^4+3*x^5) / ((1-x)^2*(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[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

PROG

(PARI) concat(0, Vec(x*(1+3*x+x^2-2*x^3-2*x^4+3*x^5)/((1-x)^2*(1+x)^2) + O(x^100))) \\ Colin Barker, Jan 11 2016

CROSSREFS

Cf. A267015.

Sequence in context: A062069 A163375 A027011 * A246011 A061023 A057690

Adjacent sequences:  A267045 A267046 A267047 * A267049 A267050 A267051

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 09 2016

STATUS

approved

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Last modified January 22 11:34 EST 2019. Contains 319363 sequences. (Running on oeis4.)