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

Yesterday's SOTD * Tomorrow's SOTD

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A001316: Gould’s sequence:

a (n) = ∑ n k  = 0  [(  nk  )  mod 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 nn  )

.