A014421 Odd elements in Pascal's triangle.

1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 5, 5, 1, 1, 15, 15, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 1, 1, 9, 9, 1, 1, 45, 45, 1, 1, 11, 55, 165, 165, 55, 11, 1, 1, 495, 495, 1, 1, 13, 715, 1287, 1287, 715, 13, 1, 1, 91, 1001, 3003, 3003, 1001, 91, 1, 1, 15, 105, 455, 1365, 3003, 5005

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn
• easy
• tabf

Comments

The number of terms of the n-row is A001316(n). - Michel Marcus, Jan 11 2016

Examples

			Triangle starts:
1;
1, 1;
1, 1;
1, 3, 3, 1;
1, 1;
1, 5, 5, 1;
1, 15, 15, 1;
1, 7, 21, 35, 35, 21, 7, 1;
...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10070 (rows 0 to 375, flattened)
• Arvind Ayyer, Amritanshu Prasad, Steven Spallone, Odd partitions in Young's lattice, arXiv:1601.01776 [math.CO], 2016. See Fig. 3.
• A. M. Reiter, Determining the dimension of fractals generated by Pascal’s triangle, Fibonacci Quart, 31(2):112-120, 1993.

Crossrefs

Cf. A001316, A007318, A014414.

Cf. A143333. [From Reinhard Zumkeller, Oct 24 2010]

Programs

Maple

select(type, [seq(seq(binomial(n,k),k=0..n),n=0..20)],odd); # Robert Israel, Jan 11 2016

Mathematica

Select[ Flatten[ Table[ Binomial[ n, i ], {n, 0, 20}, {i, 0, n} ] ], OddQ ]

PARI

tabf(nn) = {for (n=0, nn, for (k=0, n, b = binomial(n, k); if (b % 2, print1(b, ", "))); print(););} \\ Michel Marcus, Jan 11 2016

Extensions

More terms from Erich Friedman

Keyword tabl replaced by tabf by Reinhard Zumkeller, Oct 21 2010

Offset changed to 0 by Michel Marcus, Jan 11 2016