A254233 Number of ways to partition the multiset consisting of n copies each of 1, 2, and 3 into n sets of size 3.

1, 1, 4, 10, 25, 49, 103, 184, 331, 554, 911, 1424, 2204, 3278, 4817, 6896, 9746, 13487, 18480, 24882, 33192, 43683, 56994, 73512, 94131, 119340, 150300, 187732, 233065, 287248, 352153, 428944, 519949, 626737, 752095, 897994, 1067924, 1264241, 1491155, 1751672

Offset: 0

Author

Tatsuru Murai, Jan 27 2015

Keywords

• nonn
• easy

Examples

			For n = 2, the set {1,1,2,2,3,3} can be partitioned into two sets in four ways: {{112},{233}}, {{113},{223}}, {{122},{133}}, and {{123},{123}}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002135, A254243.

Column k=3 of A257462.

Formula

G.f.: (x^12-x^11+x^10+3*x^9+5*x^8+x^7+4*x^6+x^5+5*x^4+3*x^3+x^2-x+1) / ((x^2+1)*(x^2-x+1)*(x^2+x+1)^3*(x+1)^4*(x-1)^8). - Alois P. Heinz, Apr 21 2015

Extensions

Fixed definition and examples by Kellen Myers, Apr 21 2015

a(14)-a(39) from Alois P. Heinz, Apr 21 2015