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 A153490 Sierpinski carpet, read by antidiagonals. 6
 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Sierpinski carpet is the fractal obtained by starting with a unit square and at subsequent iterations, subdividing each square into 3 X 3 smaller squares and removing (from nonempty squares) the middle square. After the n-th iteration, the upper-left 3^n X 3^n squares will always remain the same. Therefore this sequence, which reads these by antidiagonals, is well-defined. Row sums are {1, 2, 2, 4, 5, 4, 6, 6, 4, 8, 10, 8, ...}. LINKS Eric Weisstein's World of Mathematics, Sierpinski Carpet. Wikipedia, Sierpinski carpet. EXAMPLE The Sierpinski carpet matrix reads    1 1 1 1 1 1 1 1 1 ...    1 0 1 1 0 1 1 0 1 ...    1 1 1 1 1 1 1 1 1 ...    1 1 1 0 0 0 1 1 1 ...    1 0 1 0 0 0 1 0 1 ...    1 1 1 0 0 0 1 1 1 ...    1 1 1 1 1 1 1 1 1 ...    1 0 1 1 0 1 1 0 1 ...    1 1 1 1 1 1 1 1 1 ...    (...) so the antidiagonals are   {1},   {1, 1},   {1, 0, 1},   {1, 1, 1, 1},   {1, 1, 1, 1, 1},   {1, 0, 1, 1, 0, 1},   {1, 1, 1, 0, 1, 1, 1},   {1, 1, 1, 0, 0, 1, 1, 1},   {1, 0, 1, 0, 0, 0, 1, 0, 1},   {1, 1, 1, 1, 0, 0, 1, 1, 1, 1},   {1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1},   {1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1},   ... MATHEMATICA << MathWorld`Fractal`; fractal = SierpinskiCarpet; a = fractal[4]; Table[Table[a[[m]][[n - m + 1]], {m, 1, n}], {n, 1, 12}]; Flatten[%] PROG (PARI) A153490_row(n, A=Mat(1))={while(#A

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)