A383868 a(n) = 2^(n-3)*(3*binomial(n,4) + 4*binomial(n,2) + 8).

1, 2, 6, 20, 70, 252, 904, 3152, 10560, 33920, 104704, 311808, 899584, 2524160, 6912000, 18526208, 48726016, 126025728, 321126400, 807403520, 2005794816, 4929093632, 11994136576, 28924968960, 69185044480, 164240556032, 387201368064, 907009851392, 2112083722240

Offset: 0

Author

Enrique Navarrete, May 12 2025

Keywords

• nonn
• easy

Comments

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

Examples

			a(2) = 6 since the strings are 01, 10, 00, 11, 22, and 33.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Crossrefs

Cf. A383778.

Programs

Mathematica

a[n_] := 2^(n-3) * (3*Binomial[n, 4] + 4*Binomial[n, 2] + 8); Array[a, 30, 0] (* Amiram Eldar, May 13 2025 *)

Formula

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

G.f.: (1 - 8*x + 26*x^2 - 40*x^3 + 30*x^4)/(1 - 2*x)^5. - Stefano Spezia, May 13 2025