A266793 Total number of ON (black) cells after n iterations of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 5, 10, 14, 21, 26, 37, 42, 57, 62, 81, 86, 109, 114, 141, 146, 177, 182, 217, 222, 261, 266, 309, 314, 361, 366, 417, 422, 477, 482, 541, 546, 609, 614, 681, 686, 757, 762, 837, 842, 921, 926, 1009, 1014, 1101, 1106, 1197, 1202, 1297, 1302, 1401, 1406

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 04 2016 and Apr 18 2019: (Start)

a(n) = (1+7*(-1)^n-2*(-3+(-1)^n)*n+2*n^2)/4 for n>3.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>8.

G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(1+x)^2).

(End)

Mathematica

rule=61; 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. A266786.

Sequence in context: A195094 A308805 A001841 * A176222 A365763 A008610

Adjacent sequences: A266790 A266791 A266792 * A266794 A266795 A266796

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved