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%I #13 Jul 20 2024 14:40:44
%S 0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0,0,1,
%T 0,0,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,1,1,1,
%U 1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,1,1
%N Triangle read by rows giving successive states of cellular automaton generated by "Rule 149" within range n from the origin.
%H Reinhard Zumkeller, <a href="/A226464/b226464.txt">Rows n = 0..120 of triangle, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F T(n,k) = 1 - A070950(n,2*n+1-k), 0 <= k <= 2*n+1.
%e Initial rows, terms moved together (all cells outside the shown range are 1):
%e . 0: 0
%e . 1: 000
%e . 2: 01100
%e . 3: 0000100
%e . 4: 011101100
%e . 5: 00010000100
%e . 6: 0110111101100
%e . 7: 000000110000100
%e . 8: 01111100011101100
%e . 9: 0001110110010000100
%e . 10: 011001000010111101100
%e . 11: 00001011110100110000100
%e . 12: 0111010011001100011101100
%e . 13: 000100110001000110010000100
%e . 14: 01101100011011100010111101100
%e . 15: 0000000110000010110100110000100
%e . 16: 011111100011110100001100011101100
%e . 17: 00011110110011001111000110010000100
%e . 18: 0110011000010001001101100010111101100
%e . 19: 000010001110111011000000110100110000100
%e . 20: 01110111001000100001111100001100011101100
%e . 21: 0001000101011101111001110111000110010000100
%e . 22: 011011101010010001101001000101100010111101100
%e . 23: 00000010010110111000011011101000110100110000100
%e . 24: 0111110110100000101110000010011100001100011101100
%e . 25: 000111000001111101001011110110010111000110010000100 .
%t A226464list[rowmax_]:=MapIndexed[ArrayPad[#1,#2-rowmax-1]&,CellularAutomaton[149,{{0},1},rowmax]];A226464list[10] (* Generates 11 rows *) (* _Paolo Xausa_, Jun 01 2023 *)
%o (Haskell)
%o a226464 n k = a226464_tabf !! n !! k
%o a226464_row n = a226464_tabf !! n
%o a226464_tabf = map reverse a226463_tabf
%Y Cf. A005408 (row lengths), A070951 (row sums), A226474 central terms), A226463 (mirror image, rule 135), A071032 (complemented, rule 86), A070950 (mirrored and complemented, rule 30).
%K nonn,tabf
%O 0
%A _Reinhard Zumkeller_, Jun 08 2013
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