The OEIS is supported by the many generous donors to the OEIS Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047929 a(n) = 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). This sequence 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. For example, no 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. - Asher Auel, 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 [math.CO], 2014-2015. 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. G.f.: 6*x^3*(3 + x)/(1 - x)^5. - Stefano Spezia, May 20 2021 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, May 22 2021 From Amiram Eldar, May 25 2021: (Start) Sum_{n>=3} 1/a(n) = (Pi^2 - 9)/12. Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/24 + 2*log(2) - 7/4. (End) MATHEMATICA Drop[CoefficientList[Series[6 x^3*(3 + x)/(1 - x)^5, {x, 0, 34}], x], 2] (* Michael De Vlieger, May 21 2021 *) 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. A004320, A045991, A233440. Sequence in context: A186122 A275253 A034725 * A243995 A264202 A338783 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)