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# Template:Sequence of the Day for March 8

Intended for: March 8, 2013

## Timetable

• First draft entered by Alonso del Arte on February 16, 2012
• Draft reviewed by Daniel Forgues on March 3, 2016
• Draft to be approved by February 8, 2013

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A001316: Gould's sequence: ${\displaystyle \textstyle {a(n)=\sum _{k=0}^{n}[{\binom {n}{k}}{\bmod {2}}]}}$.

{ 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, ... }
Essentially this counts how many odd entries there are in row
 n
of Pascal's triangle, and like the sequence of row sums, this sequence also consists entirely of powers of
 2
. Robert Wilson noticed that the first occurrence of
 2 k
is when
 n = 2 k  −  1
, while Benoit Cloitre discovered that
 a (n)
is the highest power of
 2
dividing
 (  2 n n  )
.