login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084876 Number of (k,m,n)-antichains of multisets with k=3 and m=4. 1
0, 0, 0, 310, 159300, 32389900, 4469327850, 503689260970, 50466655894200, 4701945998612200, 418104908350395750, 36055756736065208230, 3046399249526576159700, 253883533322134812268900, 20963248884482293139928450, 1720141562616331422239725090 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
By a (k,m,n)-antichain of multisets we mean an m-antichain of k-bounded multisets on an n-set. A multiset is called k-bounded if every its element has the multiplicity not greater than k-1.
LINKS
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
FORMULA
a(n) = (1/4!)*(81^n - 12*54^n + 24*42^n + 4*36^n - 24*31^n + 6*27^n + 6*26^n - 36*18^n + 36*14^n + 11*9^n - 22*6^n + 6*3^n).
G.f.: -10*x^3*(-31 - 5173*x + 663390*x^2 - 16812297*x^3 - 320866029*x^4 + 19383439320*x^5 - 243502067160*x^6 + 252158125680*x^7 + 6816687418800*x^8) / ( (6*x-1) *(54*x-1) *(42*x-1) *(3*x-1) *(9*x-1) *(27*x-1) *(31*x-1) *(26*x-1) *(18*x-1) *(81*x-1) *(36*x-1) *(14*x-1) ). - R. J. Mathar, Jul 08 2011
MATHEMATICA
Table[(81^n - 12*54^n + 24*42^n + 4*36^n - 24*31^n + 6*27^n + 6*26^n - 36*18^n + 36*14^n + 11*9^n - 22*6^n + 6*3^n)/24, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
PROG
(PARI) for(n=0, 50, print1((81^n - 12*54^n + 24*42^n + 4*36^n - 24*31^n + 6*27^n + 6*26^n - 36*18^n + 36*14^n + 11*9^n - 22*6^n + 6*3^n)/24, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(81^n - 12*54^n + 24*42^n + 4*36^n - 24*31^n + 6*27^n + 6*26^n - 36*18^n + 36*14^n + 11*9^n - 22*6^n + 6*3^n)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
CROSSREFS
Sequence in context: A218103 A289304 A281568 * A190567 A060339 A046016
KEYWORD
nonn
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Jun 10 2003
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)