A226463 Triangle read by rows giving successive states of cellular automaton generated by "Rule 135" within range n from the origin.

0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0

Offset

0

Links

Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Eric Weisstein's World of Mathematics, Rule 30

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Formula

T(n,k) = 1 - A070950(n,k), 0 <= k <= 2*n+1.

Example

Initial rows, terms moved together (all cells outside the shown range are 1):
.   0:                           0
.   1:                          000
.   2:                         00110
.   3:                        0010000
.   4:                       001101110
.   5:                      00100001000
.   6:                     0011011110110
.   7:                    001000011000000
.   8:                   00110111000111110
.   9:                  0010000100110111000
.  10:                 001101111010000100110
.  11:                00100001100101111010000
.  12:               0011011100011001100101110
.  13:              001000010011000100011001000
.  14:             00110111101000111011000110110
.  15:            0010000110010110100000110000000
.  16:           001101110001100001011110001111110
.  17:          00100001001100011110011001101111000
.  18:         0011011110100011011001000100001100110
.  19:        001000011001011000000110111011100010000
.  20:       00110111000110000111110000100010011101110
.  21:      0010000100110001110111001111011101010001000
.  22:     001101111010001101000100101100010010101110110
.  23:    00100001100101100010111011000011101101001000000
.  24:   0011011100011000011100100000111010000010110111110
.  25:  001000010011000111010011011110100101111100000111000 .

Mathematica

A226463list[rowmax_]:=MapIndexed[ArrayPad[#1, #2-rowmax-1]&, CellularAutomaton[135, {{0}, 1}, rowmax]]; A226463list[10] (* Generates 11 rows *) (* Paolo Xausa, May 31 2023 *)

Prog

(Haskell)
a226463 n k = a226463_tabf !! n !! k
a226463_row n = a226463_tabf !! n
a226463_tabf = map (map (1 -)) a070950_tabf

Crossrefs

Cf. A005408 (row lengths), A070951 (row sums), A226474 (central terms), A070950 (complemented, rule 30), A226464 (mirrored, rule 149).

Sequence in context: A011684 A011674 A011683 * A011681 A011689 A011680

Adjacent sequences: A226460 A226461 A226462 * A226464 A226465 A226466

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Jun 08 2013

Status

approved