A363591 a(n) = 3*(3^(n-1) - 2^n + 1)/2 - binomial(n,2), n >= 3.

0, 12, 65, 255, 882, 2870, 9039, 27945, 85448, 259512, 784797, 2366819, 7125198, 21424938, 64373339, 193316877, 580344132, 1741819148, 5227030665, 15684238119, 47059006250, 141189602142, 423593972775, 1270832250545, 3812597415552, 11437993573920, 34314383375669

Offset: 3

Author

Enrique Navarrete, Jun 10 2023

Keywords

• nonn
• easy

Comments

2*a(n) is the number of ordered set partitions of an n-set into 3 nonempty sets such that the number of elements in the first two sets (in total) is at least three.

Examples

			2*a(5)=130 subtracting the 20 ordered set partitions of the type {1},{2},{3,4,5} from the 150 ordered set partitions of a 5-set into 3 parts.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-24,34,-23,6).

Crossrefs

Cf. A001117, A363603.

Programs

Mathematica

LinearRecurrence[{8, -24, 34, -23, 6}, {0, 12, 65, 255, 882}, 30] (* or *)
A363591[n_] := (3^n - 3*2^n - n^2 + n + 3)/2;
Array[A363591, 30, 3] (* Paolo Xausa, Aug 30 2024 *)

Formula

G.f.: x^4*(12 - 31*x + 23*x^2 - 6*x^3)/((1 - x)^3*(1 - 2*x)*(1 - 3*x)). - Stefano Spezia, Jun 11 2023