A266595 Number of OFF (white) cells in the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 2, 5, 6, 5, 10, 5, 14, 5, 18, 5, 22, 5, 26, 5, 30, 5, 34, 5, 38, 5, 42, 5, 46, 5, 50, 5, 54, 5, 58, 5, 62, 5, 66, 5, 70, 5, 74, 5, 78, 5, 82, 5, 86, 5, 90, 5, 94, 5, 98, 5, 102, 5, 106, 5, 110, 5, 114, 5, 118, 5, 122, 5, 126, 5, 130, 5, 134, 5, 138, 5

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 02 2016 and Apr 18 2019: (Start)

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

a(n) = 2*a(n-2)-a(n-4) for n>4.

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

(End)

Mathematica

rule=37; 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[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)

Crossrefs

Cf. A266588.

Sequence in context: A261895 A112573 A233740 * A120406 A050157 A209503

Adjacent sequences: A266592 A266593 A266594 * A266596 A266597 A266598

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved