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

1,1

Links

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

Example

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
  ...

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 *)

Prog

(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())
(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

Crossrefs

Cf. A001263, A047999, A007318.

Cf. A230116 (rows seen as binary numbers).

Sequence in context: A014163 A358672 A308016 * A204183 A204177 A185917

Adjacent sequences: A166357 A166358 A166359 * A166361 A166362 A166363

Keyword

easy,nonn,tabl

Author

Gerald McGarvey, Oct 12 2009

Status

approved