Template:Sequence of the Day for November 25

Intended for: November 25, 2012

Timetable

• First draft entered by Alonso del Arte on November 26, 2011 based on comments by Philippe Deleham and Olivier Gerard ✓
• Draft reviewed by Daniel Forgues on November 24, 2019
• Draft to be approved by October 25, 2012

Thanksgiving won't fall on November 25 until the year 2021.

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

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A001788:

n  (n + 1)  2 n  − 2, n   ≥   1.

{ 1, 6, 24, 80, 240, 672, 1792, 4608, ... }

This is the sum of all elements of all non-empty subsets of

{1, 2, ..., n}

. (This is also the sum of all elements of all subsets, where for the empty subset we get the empty sum, i.e. 0.) For example,

a (3) = 24

: the subsets are {1, 2, 3}, {1, 2}, {1, 3}, {2, 3}, {1}, {2}, {3}, { } and (1 + 2 + 3) + (1 + 2) + (1 + 3) + (2 + 3) + (1) + (2) + (3) + 0 = 24.
Equivalently, this is the sum of all nodes (except the last one, equal to

n + 1

) of all integer compositions of

n + 1

. For example, the integer compositions of 4 (except 4 itself) are {1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 2 + 1, 2 + 1 + 1, 1 + 3, 3 + 1} and 6 × 4 = 24. ^{(Verify: Should it be: A006002?.)} 

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