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A266448
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Total number of ON (black) cells after n iterations of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 2, 4, 7, 11, 17, 21, 31, 35, 49, 53, 71, 75, 97, 101, 127, 131, 161, 165, 199, 203, 241, 245, 287, 291, 337, 341, 391, 395, 449, 453, 511, 515, 577, 581, 647, 651, 721, 725, 799, 803, 881, 885, 967, 971, 1057, 1061, 1151, 1155, 1249, 1253, 1351, 1355
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history;
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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
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FORMULA
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Conjectures from Colin Barker, Dec 30 2015 and Apr 16 2019: (Start)
a(n) = (2*n^2+2*n+(-1)^n*(7-2*n)+5)/4 for n>2.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7.
G.f.: (1+x+x^3+x^4+x^5-2*x^6+x^7) / ((1-x)^3*(1+x)^2).
(End)
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MATHEMATICA
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rule=25; 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. A266441.
Sequence in context: A116615 A053145 A192589 * A101978 A076273 A024455
Adjacent sequences: A266445 A266446 A266447 * A266449 A266450 A266451
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KEYWORD
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nonn,easy
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AUTHOR
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Robert Price, Dec 29 2015
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STATUS
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approved
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