A084882 Number of (k,m,n)-multiantichains of multisets with k=3 and m=5.

1, 3, 51, 4129, 1439381, 814788851, 395927618035, 155157302244381, 51960586962031617, 15663181302847575559, 4402571746033946222639, 1180812802393866826858193, 306839347397532891662028733

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

Keywords

• nonn

Comments

By a (k,m,n)-multiantichain of multisets we mean an m-multiantichain of k-bounded multisets on an n-set. The elements of a multiantichain could have the multiplicities greater than 1. 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..415
• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.

Crossrefs

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

Programs

Mathematica

Table[(1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 30*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 360*54^n + 720*42^n + 120*36^n - 720*31^n + 275*27^n + 180*26^n - 1650*18^n + 1650*14^n + 870*9^n - 1740*6^n + 744*3^n), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

Formula

a(n) = (1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 30*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 360*54^n + 720*42^n + 120*36^n - 720*31^n + 275*27^n + 180*26^n - 1650*18^n + 1650*14^n + 870*9^n - 1740*6^n + 744*3^n).