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A266447
Number of ON (black) cells in the n-th iteration of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
1
1, 1, 2, 3, 4, 6, 4, 10, 4, 14, 4, 18, 4, 22, 4, 26, 4, 30, 4, 34, 4, 38, 4, 42, 4, 46, 4, 50, 4, 54, 4, 58, 4, 62, 4, 66, 4, 70, 4, 74, 4, 78, 4, 82, 4, 86, 4, 90, 4, 94, 4, 98, 4, 102, 4, 106, 4, 110, 4, 114, 4, 118, 4, 122, 4, 126, 4, 130, 4, 134, 4, 138
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Dec 30 2015 and Apr 16 2019: (Start)
a(n) = n-(-1)^n*(n-4) for n>3.
a(n) = 2*a(n-2)-a(n-4) for n>7.
G.f.: (1+x+x^3+x^4+x^5-2*x^6+x^7) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=25; 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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)
CROSSREFS
Cf. A266441.
Sequence in context: A102284 A273098 A328166 * A100700 A361478 A332781
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 29 2015
STATUS
approved