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

0,8

Comments

Row sums are A088560.

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

Links

Reinhard Zumkeller, Rows n = 0..127 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

Formula

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

Example

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;

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A122850 A132062 A065547 * A283798 A065551 A283797

Adjacent sequences: A143330 A143331 A143332 * A143334 A143335 A143336

Keyword

nonn,tabl,easy,look

Author

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

Extensions

Offset set to 0 by Reinhard Zumkeller, Oct 21 2010

Status

approved