

A263807


Total number of ON (black) cells after n iterations of the "Rule 157" elementary cellular automaton starting with a single ON (black) cell.


2



1, 3, 6, 11, 17, 25, 34, 45, 57, 71, 86, 103, 121, 141, 162, 185, 209, 235, 262, 291, 321, 353, 386, 421, 457, 495, 534, 575, 617, 661, 706, 753, 801, 851, 902, 955, 1009, 1065, 1122, 1181, 1241, 1303, 1366, 1431, 1497, 1565, 1634, 1705, 1777, 1851, 1926
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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 20 2016 and Apr 16 2019: (Start)
a(n) = 2*a(n1)2*a(n3)+a(n4) for n>3.
G.f.: (1+x+x^3) / ((1x)^3*(1+x)).
(End)


MATHEMATICA

rule=157; 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 *) 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. A263804.
Sequence in context: A022775 A025743 A022338 * A176708 A273140 A320272
Adjacent sequences: A263804 A263805 A263806 * A263808 A263809 A263810


KEYWORD

nonn,easy


AUTHOR

Robert Price, Jan 17 2016


STATUS

approved



