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A266811
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Total number of ON (black) cells after n iterations of the "Rule 62" elementary cellular automaton starting with a single ON (black) cell.
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2
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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
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OFFSET
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0,2
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Robert Price, Jan 03 2016
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STATUS
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approved
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