A266594 Total number of ON (black) cells after n iterations of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 5, 7, 10, 16, 19, 29, 32, 46, 49, 67, 70, 92, 95, 121, 124, 154, 157, 191, 194, 232, 235, 277, 280, 326, 329, 379, 382, 436, 439, 497, 500, 562, 565, 631, 634, 704, 707, 781, 784, 862, 865, 947, 950, 1036, 1039, 1129, 1132, 1226, 1229, 1327, 1330, 1432

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) = (n^2-(-1)^n*(n-3)+5)/2 for n>0.

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

G.f.: (1+x+x^2-2*x^4+3*x^5) / ((1-x)^3*(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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)

Crossrefs

Cf. A266588.

Sequence in context: A159942 A102339 A172410 * A103871 A068817 A156779

Adjacent sequences: A266591 A266592 A266593 * A266595 A266596 A266597

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved