A143333 Pascal's triangle binomial(n,m) read by rows, all even elements replaced by zero.

1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 0, 0, 0, 1, 1, 5, 0, 0, 5, 1, 1, 0, 15, 0, 15, 0, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 9, 0, 0, 0, 0, 0, 0, 9, 1, 1, 0, 45, 0, 0, 0, 0, 0, 45, 0, 1

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 21 2008

Keywords

• nonn
• tabl
• easy
• look

Comments

Row sums are A088560.

A047999(n,k) = A057427(T(n,k)). - Reinhard Zumkeller, Oct 24 2010

Examples

			The triangle starts in row n=0 with columns 0<=m<=n as:
  1;
  1,  1;
  1,  0,  1;
  1,  3,  3,  1;
  1,  0,  0,  0,  1;
  1,  5,  0,  0,  5,  1;
  1,  0, 15,  0, 15,  0,  1;
  1,  7, 21, 35, 35, 21,  7,  1;
  1,  0,  0,  0,  0,  0,  0,  0,  1;
  1,  9,  0,  0,  0,  0,  0,  0,  9,  1;
  1,  0, 45,  0,  0,  0,  0,  0, 45,  0,  1;
		

Links

• Reinhard Zumkeller, Rows n = 0..127 of triangle, flattened
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A007318, A014421, A047999, A088560. - Reinhard Zumkeller, Oct 24 2010

Programs

Haskell

a143333 n k = a143333_tabl !! (n-1) !! (k-1)
a143333_row n = a143333_tabl !! (n-1)
a143333_tabl = zipWith(zipWith (*)) a007318_tabl a047999_tabl
-- Reinhard Zumkeller, Oct 10 2013

Mathematica

t[n_, m_] = Mod[Binomial[n, m], 2]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

T(n,m) = A047999(n,m)*A007318(n,m).

Extensions

Offset set to 0 by Reinhard Zumkeller, Oct 21 2010