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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
The number of 0's in row n is A071052(n), and the number of 1's in row n is A071053(n). - Michael Somos, Jun 24 2018
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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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Robert Price, Table of n, a(n) for n = 0..9999
Rémy Sigrist, Representation of the first 2^10 rows of the table
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
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FORMULA
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a(n) = A027907(n) modulo 2. - Michel Marcus, Mar 20 2014
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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;
... - Michel Marcus, Mar 20 2014
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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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Cf. A027907, A071052, A071053.
This sequence, A038184 and A118110 are equivalent descriptions of the Rule 150 automaton.
Sequence in context: A344864 A140653 A342892 * A071038 A131522 A221641
Adjacent sequences: A071033 A071034 A071035 * A071037 A071038 A071039
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KEYWORD
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nonn,tabf
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AUTHOR
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Hans Havermann, May 26 2002
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EXTENSIONS
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Corrected by Hans Havermann, Jan 08 2012
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STATUS
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approved
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