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Row sums of a signed Thue-Morse related triangle.
2

%I #7 Aug 04 2023 04:35:07

%S 1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,

%T 1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,

%U 1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,1

%N Row sums of a signed Thue-Morse related triangle.

%C 0's occur at positions indexed by the odious numbers given by A091855.

%F a(n) = A127246(n) mod 2.

%F a(n) = Sum_{k=0..n} ((-1)^(n-k) * Product_{j=0..n-k-1} A010060(n-j)).

%t a[n_] := Mod[Sum[Product[ThueMorse[i], {i, k+1, n}], {k, 0, n}], 2]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 04 2023 *)

%Y Row sums of A127244.

%Y Cf. A000069, A010060, A091855, A127246.

%K easy,nonn

%O 0,1

%A _Paul Barry_, Jan 10 2007

%E More terms from _Amiram Eldar_, Aug 04 2023