

A266977


Number of ON (black) cells in the nth iteration of the "Rule 78" elementary cellular automaton starting with a single ON (black) cell.


4



1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36
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OFFSET

0,2


COMMENTS

Also, a(n1) is the number of topologically inequivalent opening moves in the Sprouts game on n nodes [Browne].  Andrey Zabolotskiy, Feb 12 2020


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
Cameron B. Browne, Boundary Matching for Interactive Sprouts, in: ACG 2015, pp. 147159, LNCS 9525, Springer, doi:10.1007/9783319279923_14.
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

From Colin Barker, Jan 08 2016 and Apr 16 2019: (Start)
a(n) = (2*n+(1)^n+7)/4 for n>0.
a(n) = a(n1)+a(n2)a(n3) for n>3.
G.f.: (1+xx^3) / ((1x)^2*(1+x)).
(End)


MATHEMATICA

rule=78; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rowsk+1, rows+k1}], {k, 1, rows}]; (* Truncated list of each row *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)


CROSSREFS

Cf. A266974, A004526.
Sequence in context: A005410 A120835 A091374 * A065603 A225215 A214672
Adjacent sequences: A266974 A266975 A266976 * A266978 A266979 A266980


KEYWORD

nonn,easy


AUTHOR

Robert Price, Jan 07 2016


STATUS

approved



