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 A070909 Triangle read by rows giving successive states of cellular automaton generated by "Rule 28" and by "Rule 156". 13
 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row n has length n+1. Contribution from Gary W. Adamson, May 15 2010: (Start) Eigensequence of the triangle = A038754. (i.e. 1, 1, 2, 3, 6, 9, 18,...) shifts to the left with multiplication by triangle A070909. Binomial transform of A070909 = triangle A177953. (End) Contribution from Paul Barry, Nov 03 2010: (Start) Generalized (conditional) Riordan array with k-th column generated by If(mod(k,2)=0,x^k/(1-x),x^k). A181651 is an eigentriangle. Inverse is A181650. (End) REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3. LINKS Eric Weisstein's World of Mathematics, Rule 28 EXAMPLE Contribution from Paul Barry, Nov 03 2010: (Start) Triangle begins 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, Production matrix begins 1, 1, 0, -1, 1, 0, -1, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1 (End) MATHEMATICA rows = 14; ca = CellularAutomaton[28, {{1}, 0}, rows-1]; Flatten[Table[ca[[k, 1 ;; k]], {k, 1, rows}]] (* Jean-François Alcover, May 24 2012 *) CROSSREFS Cf. A038754, A070909 [From Gary W. Adamson, May 15 2010] Sequence in context: A113998 A253084 A182741 * A115954 A115526 A239681 Adjacent sequences:  A070906 A070907 A070908 * A070910 A070911 A070912 KEYWORD nonn,tabl AUTHOR Hans Havermann, May 26 2002 STATUS approved

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Last modified February 16 15:55 EST 2020. Contains 331961 sequences. (Running on oeis4.)