A084875 Number of (k,m,n)-antichains of multisets with k=3 and m=3.

0, 0, 1, 350, 24025, 1061570, 38306701, 1238697950, 37547263825, 1093418309690, 31035659056501, 866306577308150, 23915774118612025, 655397866616830610, 17872808187862527901, 485794481046271815950, 13175146525408965630625

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

Keywords

• nonn

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

• G. C. Greubel, Table of n, a(n) for n = 0..695
• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
• Index entries for linear recurrences with constant coefficients, signature (77,-2277,32895,-242514,854388,-1102248).

Crossrefs

Cf. A016269, A047707, A051112-A051118, A084869-A084883.

Programs

Magma

[(27^n - 6*18^n + 6*14^n + 3*9^n - 6*6^n + 2*3^n)/6: n in [0..50]]; // G. C. Greubel, Oct 08 2017

Mathematica

Table[(27^n - 6*18^n + 6*14^n + 3*9^n - 6*6^n + 2*3^n)/6, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
LinearRecurrence[{77,-2277,32895,-242514,854388,-1102248},{0,0,1,350,24025,1061570},20] (* Harvey P. Dale, May 29 2025 *)

PARI

for(n=0,50, print1((27^n - 6*18^n + 6*14^n + 3*9^n - 6*6^n + 2*3^n)/6, ", ")) \\ G. C. Greubel, Oct 08 2017

Formula

a(n) = (1/3!)*(27^n - 6*18^n + 6*14^n + 3*9^n - 6*6^n + 2*3^n).

G.f.: -x^2*(-1-273*x+648*x^2+24300*x^3) / ( (18*x-1)*(9*x-1)*(6*x-1)*(3*x-1)*(14*x-1)*(27*x-1) ). - R. J. Mathar, Jul 08 2011