A383778 a(n) = n*(n^2 - 3*n + 10)*2^(n-4).

0, 1, 4, 15, 56, 200, 672, 2128, 6400, 18432, 51200, 137984, 362496, 931840, 2351104, 5836800, 14286848, 34537472, 82575360, 195493888, 458752000, 1067974656, 2468347904, 5667553280, 12935233536, 29360128000, 66303557632, 149032009728, 333531054080, 743431995392

Offset: 0

Author

Enrique Navarrete, May 09 2025

Keywords

• nonn
• easy

Comments

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

Examples

			a(3) = 15 since the strings are 322 (3 of this type), 300 (3 of this type), 311 (3 of this type), and 301 (6 of this type).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A060354.

Programs

Mathematica

a[n_] := n*(n^2-3*n+10)*2^(n-4); Array[a, 30, 0] (* Amiram Eldar, May 09 2025 *)

Formula

E.g.f.: x*(1 + x^2/2)*exp(2*x).

G.f.: x*(1 - 4*x + 7*x^2)/(1 - 2*x)^4. - Stefano Spezia, May 10 2025