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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
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 (list; graph; refs; listen; history; text; internal format)
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: (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 *)

PROG

(PARI) Vec((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)) + O(x^100)) \\ Colin Barker, Jan 04 2016

CROSSREFS

Cf. A071031.

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

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)