A267049 Total number of OFF (white) cells after n iterations of the "Rule 91" elementary cellular automaton starting with a single ON (black) cell.

0, 1, 4, 7, 11, 14, 22, 25, 37, 40, 56, 59, 79, 82, 106, 109, 137, 140, 172, 175, 211, 214, 254, 257, 301, 304, 352, 355, 407, 410, 466, 469, 529, 532, 596, 599, 667, 670, 742, 745, 821, 824, 904, 907, 991, 994, 1082, 1085, 1177, 1180, 1276, 1279, 1379, 1382

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

Formula

Conjectures from Colin Barker, Jan 11 2016 and Apr 19 2019: (Start)

a(n) = (n^2+(-1)^n*(n-3)+5)/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.: x*(1+3*x+x^2-2*x^3-2*x^4+3*x^5) / ((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 *) 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. A267015.

Sequence in context: A310733 A310734 A190774 * A310735 A003670 A084390

Adjacent sequences: A267046 A267047 A267048 * A267050 A267051 A267052

Keyword

nonn

Author

Robert Price, Jan 09 2016

Status

approved