A266438 Total number of ON (black) cells after n iterations of the "Rule 23" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 4, 11, 11, 22, 22, 37, 37, 56, 56, 79, 79, 106, 106, 137, 137, 172, 172, 211, 211, 254, 254, 301, 301, 352, 352, 407, 407, 466, 466, 529, 529, 596, 596, 667, 667, 742, 742, 821, 821, 904, 904, 991, 991, 1082, 1082, 1177, 1177, 1276, 1276, 1379, 1379

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..500

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

Conjectured g.f.: (-(1 + x)^(-2) + (-3 + 3*x - 2*x^2)/(-1 + x)^3)/2. - Michael De Vlieger, Dec 29 2015

Conjectures from Colin Barker, Dec 30 2015 and Apr 15 2019: (Start)

a(n) = (n^2+2*n-(-1)^n*(n+1)+3)/2.

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

(End)

Mathematica

rule=23; 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. A266434.

Sequence in context: A107856 A212102 A168373 * A128499 A325859 A265206

Adjacent sequences: A266435 A266436 A266437 * A266439 A266440 A266441

Keyword

nonn,easy

Author

Robert Price, Dec 29 2015

Status

approved