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, 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

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: A053618 A268345 A357388 * A032801 A332641 A033818

Adjacent sequences: A267044 A267045 A267046 * A267048 A267049 A267050

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Status

approved