A266627 Total number of ON (black) cells after n iterations of the "Rule 45" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 6, 8, 13, 20, 28, 36, 43, 56, 65, 77, 88, 106, 121, 139, 153, 176, 192, 214, 229, 259, 282, 305, 325, 361, 379, 409, 441, 471, 501, 535, 563, 600, 633, 677, 704, 756, 781, 834, 866, 913, 951, 1005, 1033, 1095, 1131, 1188, 1226, 1287, 1330, 1389, 1428

Offset

0,2

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

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

Mathematica

rule=45; 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. A266619.

Sequence in context: A356217 A294862 A087327 * A289753 A002511 A074383

Adjacent sequences: A266624 A266625 A266626 * A266628 A266629 A266630

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Status

approved