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A166360 Triangle of Narayana numbers mod 2, T(n,k) = A001263(n,k) mod 2, read by rows.

%I A166360 #12 May 13 2025 02:40:20
%S A166360 1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,
%T A166360 0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,
%U A166360 0,1,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1
%N A166360 Triangle of Narayana numbers mod 2, T(n,k) = A001263(n,k) mod 2, read by rows.
%H A166360 Reinhard Zumkeller, <a href="/A166360/b166360.txt">Rows n = 1..120 of triangle, flattened</a>
%e A166360 Triangle begins:
%e A166360   1
%e A166360   1 1
%e A166360   1 1 1
%e A166360   1 0 0 1
%e A166360   1 0 0 0 1
%e A166360   1 1 0 0 1 1
%e A166360   1 1 1 1 1 1 1
%e A166360   1 0 0 0 0 0 0 1
%e A166360   1 0 0 0 0 0 0 0 1
%e A166360   1 1 0 0 0 0 0 0 1 1
%e A166360   1 1 1 0 0 0 0 0 1 1 1
%e A166360   1 0 0 1 0 0 0 0 1 0 0 1
%e A166360   1 0 0 0 1 0 0 0 1 0 0 0 1
%e A166360   1 1 0 0 1 1 0 0 1 1 0 0 1 1
%e A166360   1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A166360   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
%e A166360   ...
%t A166360 T[n_, k_] := Mod[Binomial[n-1, k-1] * Binomial[n, k-1] / k, 2]; Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 13 2025 *)
%o A166360 (PARI) p = 2; s=14; NT = matrix(s,s,n,k, binomial(n-1, k-1)*binomial(n, k-1)/k);
%o A166360 NTMP = matrix(s,s,n,k, NT[n,k]%p);
%o A166360 for(n=1,s,for(k=1,n,print1(NTMP[n,k]," "));print())
%o A166360 (Haskell)
%o A166360 a166360 n k = a166360_tabl !! (n-1) !! (k-1)
%o A166360 a166360_row n = a166360_tabl !! (n-1)
%o A166360 a166360_tabl = map (map (flip mod 2)) a001263_tabl
%o A166360 -- _Reinhard Zumkeller_, Oct 10 2013
%Y A166360 Cf. A001263, A047999, A007318.
%Y A166360 Cf. A230116 (rows seen as binary numbers).
%K A166360 easy,nonn,tabl
%O A166360 1,1
%A A166360 _Gerald McGarvey_, Oct 12 2009