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

0,7

Comments

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

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.

Example

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;
...

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 ]

Prog

(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

Crossrefs

Cf. A001316, A007318, A014414.

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

Sequence in context: A016554 A046533 A046532 * A127197 A114231 A079075

Adjacent sequences: A014418 A014419 A014420 * A014422 A014423 A014424

Keyword

nonn,easy,tabf

Author

Mohammad K. Azarian

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

Status

approved