A384243 a(n) = 2^(n-6)*n*(n^3 - 6*n^2 + 19*n - 14).

0, 0, 1, 6, 30, 140, 600, 2352, 8512, 28800, 92160, 281600, 827904, 2356224, 6522880, 17633280, 46694400, 121438208, 310837248, 784465920, 1954938880, 4816896000, 11747721216, 28386000896, 68010639360, 161690419200, 381681664000, 895098028032, 2086448136192, 4836200284160

Offset: 0

Author

Enrique Navarrete, May 23 2025

Keywords

• nonn
• easy

Comments

a(n) is the number of strings of length n defined on {0, 1, 2, 3} that have exactly two 2's, zero or two 3's, and have no restriction on the number of 0's and 1's.

Examples

			a(4) = 30 since the strings are the 6 permutations of 2233, the 6 permutations of 1122, the 6 permutations of 0022, and the 12 permutations of 0122.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Crossrefs

Cf. A060354, A327319, A383778.

Programs

Mathematica

A384243[n_] := 2^(n-6)*n*(n-1)*(n*(n-5)+14); Array[A384243, 30, 0] (* or *)
LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 1, 6, 30}, 30] (* Paolo Xausa, May 27 2025 *)

Formula

E.g.f.: exp(2*x)*(x^2/2 + x^4/4).

G.f.: x^2*(1 - 4*x + 10*x^2)/(1 - 2*x)^5. - Stefano Spezia, May 23 2025