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A266304
Total number of OFF (white) cells after n iterations of the "Rule 15" elementary cellular automaton starting with a single ON (black) cell.
2
0, 1, 5, 6, 14, 15, 27, 28, 44, 45, 65, 66, 90, 91, 119, 120, 152, 153, 189, 190, 230, 231, 275, 276, 324, 325, 377, 378, 434, 435, 495, 496, 560, 561, 629, 630, 702, 703, 779, 780, 860, 861, 945, 946, 1034, 1035, 1127, 1128, 1224, 1225, 1325, 1326, 1430
OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Dec 28 2015 and Apr 15 2019: (Start)
a(n) = n*(n+(-1)^n+2)/2.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4.
G.f.: x*(1+4*x-x^2) / ((1-x)^3*(1+x)^2). (End)
a(n) = Sum_{i=1..n} (n-i-1) mod 2. - Wesley Ivan Hurt, Sep 15 2017
MATHEMATICA
rule=15; 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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)
CROSSREFS
Cf. A266300.
Sequence in context: A084381 A289895 A335785 * A359329 A308839 A099330
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
STATUS
approved