OFFSET
0,2
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..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (18,-99,162).
FORMULA
a(n) = (9^n - 2*6^n + 3*3^n)/2.
G.f.: ( -1 + 15*x - 63*x^2 ) / ( (6*x-1)*(3*x-1)*(9*x-1) ). - R. J. Mathar, Jul 08 2011
E.g.f.: (exp(9*x) - 2*exp(6*x) + 3*exp(3*x))/2. - G. C. Greubel, Oct 08 2017
MATHEMATICA
Table[(9^n - 2*6^n + 3*3^n)/2, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
PROG
(PARI) for(n=0, 50, print1((9^n - 2*6^n + 3*3^n)/2, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(9^n - 2*6^n + 3*3^n)/2: n in [0..50]]; // G. C. Greubel, Oct 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Jun 10 2003
STATUS
approved