login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047929 n^2*(n-1)*(n-2). 5
0, 18, 96, 300, 720, 1470, 2688, 4536, 7200, 10890, 15840, 22308, 30576, 40950, 53760, 69360, 88128, 110466, 136800, 167580, 203280, 244398, 291456, 345000, 405600, 473850, 550368, 635796, 730800, 836070, 952320, 1080288, 1220736 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

There are 5 ways to put parentheses in the expression a - b - c - d: (a - (b - c)) - d, ((a - b) - c) - d, (a - b) - (c - d), a - (b - (c - d)), a - ((b - c) - d). A047929 describes how many sets of natural numbers [a,b,c,d] can be produced with the numbers {0,1,2,3,...n} such that all the distinct expressions take different values. A045991 describes the similar process for a - b - c. - Asher Natan Auel (auela(AT)reed.edu), Jan 26 2000

For n>=3, a(n)/6 is the number of permutations of n symbols that 3-commute with an n-cycle (see A233440 for definition). - Luis Manuel Rivera Martínez, Feb 24 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

Index entries for sequences related to parenthesizing

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = A004320(n-2)*6.

EXAMPLE

For example, no such sets can be produced with only 0's or only 0's and 1's; with {0,1,2,3}, 18 such sets can be produced.

PROG

(MAGMA) [n^2*(n-1)*(n-2): n in [2..40]]; // Vincenzo Librandi, May 02 2011

(PARI) a(n)=n^4 - 3*n^3 + 2*n^2 \\ Charles R Greathouse IV, May 02, 2011

CROSSREFS

Cf. A045991.

Sequence in context: A186122 A275253 A034725 * A243995 A264202 A324304

Adjacent sequences:  A047926 A047927 A047928 * A047930 A047931 A047932

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)