Template:Sequence of the Day for August 16

Intended for: August 16, 2011

Timetable

• First draft entered by Alonso del Arte on May 29, 2011 ✓
• Draft reviewed by Alonso del Arte on July 16, 2011 ✓
• Draft approved by Daniel Forgues on July 20, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A005910: Truncated octahedral numbers:

16 n 3  −  33 n 2 + 24 n  −  6, n   ≥   1.

{ 1, 38, 201, 586, 1289, 2406, 4033, ... }

You can obtain these by taking the octahedral number

Oct 3n  − 2 = k (2 k 2 + 1) 3  |3n  − 2

and cutting off the [square] pyramidal number

Pyr (4) n  − 1 = k (k + 1)  (2 k + 1) 6  |n  − 1

from each of the six vertices, i.e.

16 n 3 − 33 n 2 + 24 n − 6  =  Oct 3n  − 2 − 6 ⋅  Pyr (4) n −1, n ≥ 1.

(This description is thanks to Conway and Guy in their landmark Book of Numbers.)