A084879 Number of (k,m,n)-multiantichains of multisets with k=3 and m=2.

1, 3, 18, 189, 2106, 22113, 220158, 2114829, 19853586, 183662073, 1683014598, 15327998469, 139038783066, 1257874611633, 11360039237838, 102475402586109, 923689049088546, 8321664384098793, 74945758272961878, 674816500839877749

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

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

Sequence in context: A323502 A365996 A326088 * A141118 A033030 A279843

Adjacent sequences: A084876 A084877 A084878 * A084880 A084881 A084882

Keyword

nonn

Author

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

Status

approved