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 A319610 a(n) is the minimal number of successive OFF cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell. 2
 0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS OFF cells outside the triangle of active cells are ignored. LINKS Table of n, a(n) for n=0..138. Charlie Neder, Repeating pattern of length-1 runs Index entries for linear recurrences with constant coefficients, signature (1). FORMULA G.f.: x (x + x/(1 - x) + x^3 + x^5 + x^7) (conjectured). For n > 9, a(n)=1 at least up to n = 20000. It is conjectured that for all n>=10, a(n)=1. A period-4 pattern of length-1 runs starting at row 26 forces a(n) = 1 for all n >= 26 (see image). - Charlie Neder, Dec 15 2018 EXAMPLE The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle: 1 . a(1)= (0) 2 . . . a(2)= (0) 3 . . 0 0 . a(3)= (2) 4 . . 0 . . . . a(4)= (1) 5 . . 0 0 . 0 0 0 . a(5)= (2) 6 . . 0 . . . . 0 . . . a(6)= (1) 7 . . 0 0 . 0 0 0 0 . 0 0 . a(7)= (2) 8 . . 0 . . . . 0 0 . . . . . . a(8)= (1) 9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 . a(9)= (2) 10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . . a(10)=(1) 11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 . a(11)=(1) 12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . . a(12)=(1) 13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 . a(13)=(1) MATHEMATICA CellularAutomaton[30, {{1}, 0}, 200]; (Reverse[Internal`DeleteTrailingZeros[Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %; Table[Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Min, {i, 1, % // Length}] CROSSREFS Cf. A100053. Sequence in context: A280535 A221171 A333688 * A288739 A111621 A326398 Adjacent sequences: A319607 A319608 A319609 * A319611 A319612 A319613 KEYWORD nonn AUTHOR Philipp O. Tsvetkov, Sep 24 2018 STATUS approved

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Last modified September 15 03:00 EDT 2024. Contains 375931 sequences. (Running on oeis4.)