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%I #34 May 26 2023 08:50:20
%S 0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,
%T 0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,1,0,1,1,1,1,1,0,1,0,0,0,
%U 0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,1
%N Triangle read by rows: T(n,k) = 1 - A047999(n,k), 0 <= k <= n.
%C Sierpinski's triangle complemented.
%H Reinhard Zumkeller, <a href="/A219463/b219463.txt">Rows n = 0..128 of triangle, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiSieve.html">Sierpinski Sieve</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sierpinski_triangle">Sierpinski triangle</a>
%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F T(n,k) = if T(n-1,k-1) = T(n-1,k) then 1 else 0, 0 < k < n.
%e The triangle begins:
%e 0: 0
%e 1: 0 0
%e 2: 0 1 0
%e 3: 0 0 0 0
%e 4: 0 1 1 1 0
%e 5: 0 0 1 1 0 0
%e 6: 0 1 0 1 0 1 0
%e 7: 0 0 0 0 0 0 0 0
%e 8: 0 1 1 1 1 1 1 1 0
%e 9: 0 0 1 1 1 1 1 1 0 0
%e 10: 0 1 0 1 1 1 1 1 0 1 0
%e 11: 0 0 0 0 1 1 1 1 0 0 0 0
%e 12: 0 1 1 1 0 1 1 1 0 1 1 1 0
%e 13: 0 0 1 1 0 0 1 1 0 0 1 1 0 0
%e 14: 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
%e 15: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%t A219463row[n_]:=Sign[BitAnd[Range[0, n], -1-n]];Array[A219463row,20,0] (* _Paolo Xausa_, May 22 2023 *)
%o (Haskell)
%o a219463 n k = a219463_tabl !! n !! k :: Int
%o a219463_row n = a219463_tabl !! n
%o a219463_tabl = map (map (1 -)) a047999_tabl
%o (PARI) T(n,k)= bitand(n-k, k) != 0; \\ _Joerg Arndt_, May 22 2023
%Y Cf. A000004 (left and right edges), A057427 (central terms), A048967 (row sums = number of ones per row), A001316 (number of zeros per row), A219843 (rows as binary numbers).
%K nonn,tabl
%O 0
%A _Reinhard Zumkeller_, Nov 30 2012
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