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A084880 Number of (k,m,n)-multiantichains of multisets with k=3 and m=3. 0
1, 3, 28, 701, 28156, 1105553, 38746288, 1242925421, 37586964436, 1093785614153, 31039025026648, 866337233127941, 23916052195646716, 655400382364459553, 17872830907936220608, 485794685997062639261, 13175148372787020760996 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..16.

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).

FORMULA

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

G.f.: (1 - 74*x + 2074*x^2 - 27519*x^3 + 181764*x^4 - 514188*x^5) / ( (18*x-1)*(9*x-1)*(6*x-1)*(3*x-1)*(14*x-1)*(27*x-1) ). - R. J. Mathar, Jul 08 2011

a(0)=1, a(1)=3, a(2)=28, a(3)=701, a(4)=28156, a(5)=1105553, a(n) = 77*a(n-1) - 2277*a(n-2) + 32895*a(n-3) - 242514*a(n-4) + 854388*a(n-5) - 1102248*a(n-6). - Harvey P. Dale, Apr 08 2015

MATHEMATICA

LinearRecurrence[{77, -2277, 32895, -242514, 854388, -1102248}, {1, 3, 28, 701, 28156, 1105553}, 20] (* Harvey P. Dale, Apr 08 2015 *)

Table[(27^n - 6*18^n + 6*14^n + 9*9^n - 18*6^n + 14*3^n)/6, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

PROG

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

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

CROSSREFS

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

Sequence in context: A174483 A092985 A181588 * A110259 A276745 A015474

Adjacent sequences:  A084877 A084878 A084879 * A084881 A084882 A084883

KEYWORD

nonn

AUTHOR

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

STATUS

approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)