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%I #14 Jul 28 2023 04:08:06
%S 1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,
%T 1,1,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,0,1,
%U 0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0
%N Triangle read by rows: interleaving successive pairs of rows of Sierpiński's triangle.
%C A105321(n) = number of ones in row n;
%C A249304(n) = number of zeros in row n;
%C numbers, when rows are concatenated: A249183, A249184.
%H Reinhard Zumkeller, <a href="/A249133/b249133.txt">Table of n, a(n) for n = 0..10200</a>
%F T(n,k) = A249095(n,k) mod 2.
%e . 0: 1
%e . 1: 1 1 1
%e . 2: 1 1 0 1 1
%e . 3: 1 1 1 0 1 1 1
%e . 4: 1 1 0 1 0 1 0 1 1
%e . 5: 1 1 1 0 0 0 0 0 1 1 1
%e . 6: 1 1 0 1 1 0 0 0 1 1 0 1 1
%e . 7: 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
%e . 8: 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1
%e . 9: 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
%e . 10: 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
%e . 11: 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1
%e . 12: 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1
%e . 13: 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1
%e . 14: 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1
%e . 15: 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
%e . 16: 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 .
%t row[n_] := Mod[Riffle[Binomial[n, Range[0, n]], Binomial[n - 1, Range[0, n - 1]]], 2]; Table[row[n], {n, 0, 10}] // Flatten (* _Amiram Eldar_, Jul 28 2023 *)
%o (Haskell)
%o a249133 n k = a249133_tabf !! n !! k
%o a249133_row n = a249133_tabf !! n
%o a249133_tabf = map (map (flip mod 2)) a249095_tabf
%Y Cf. A005408 (row lengths), A105321 (row sums), A249095, A249304, A249183, A249184, A047999 (Sierpiński).
%K nonn,tabf
%O 0
%A _Reinhard Zumkeller_, Nov 14 2014