A266811 Total number of ON (black) cells after n iterations of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.

1, 4, 7, 13, 18, 26, 35, 45, 55, 69, 82, 97, 113, 131, 149, 170, 190, 213, 237, 262, 287, 316, 344, 374, 405, 438, 471, 507, 542, 580, 619, 659, 699, 743, 786, 831, 877, 925, 973, 1024, 1074, 1127, 1181, 1236, 1291, 1350, 1408, 1468, 1529, 1592, 1655, 1721

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

Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,-1,0,-1,1).

Formula

From Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)

a(n) = a(n-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.

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

(End)

Mathematica

rule=62; 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. A071031, A266813 (total OFF cells).

Partial sums of A071047.

Sequence in context: A310823 A074136 A310824 * A085787 A111710 A191138

Adjacent sequences: A266808 A266809 A266810 * A266812 A266813 A266814

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved