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A071036
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Triangle read by rows giving successive states of cellular automaton generated by "Rule 150" when started with a single ON cell.
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7
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1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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Row n has length 2n+1.
Also the coefficients of (x^2 + x + 1)^n mod 2. - Alan DenAdel, Mar 19 2014
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
1, 1, 1;
1, 0, 1, 0, 1;
1, 1, 0, 1, 0, 1, 1;
1, 0, 0, 0, 1, 0, 0, 0, 1;
1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1;
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MATHEMATICA
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T[ n_, k_] := T[n, k] = Which[k < 0 || k > 2 n, 0, n == k == 0, 1, True, Mod[ T[n - 1, k - 2] + T[n - 1, k - 1] + T[n - 1, k], 2]]; (* Michael Somos, Jun 24 2018 *)
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PROG
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(PARI) rown(n) = Vec(lift((x^2 + x + 1)^n * Mod(1, 2))); \\ Michel Marcus, Mar 20 2014
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CROSSREFS
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This sequence, A038184 and A118110 are equivalent descriptions of the Rule 150 automaton.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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