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

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, 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, 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

Offset: 1

Author

Gerald McGarvey, Oct 12 2009

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
  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 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 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
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  ...
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Crossrefs

Cf. A001263, A047999, A007318.

Cf. A230116 (rows seen as binary numbers).

Programs

Haskell

a166360 n k = a166360_tabl !! (n-1) !! (k-1)
a166360_row n = a166360_tabl !! (n-1)
a166360_tabl = map (map (flip mod 2)) a001263_tabl
-- Reinhard Zumkeller, Oct 10 2013

Mathematica

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 *)

PARI

p = 2; s=14; NT = matrix(s,s,n,k, binomial(n-1, k-1)*binomial(n, k-1)/k);
NTMP = matrix(s,s,n,k, NT[n,k]%p);
for(n=1,s,for(k=1,n,print1(NTMP[n,k]," "));print())