A383623 a(n) = 4^n - (n^2 + 3*n + 4)*2^(n-2).

0, 0, 2, 20, 128, 672, 3168, 14016, 59648, 247808, 1014272, 4113408, 16588800, 66674688, 267444224, 1071497216, 4289921024, 17168596992, 68694441984, 274822594560, 1099389992960, 4397780172800, 17591605133312, 70367481692160, 281472242024448

Offset: 0

Author

Enrique Navarrete, May 03 2025

Keywords

• nonn
• easy

Comments

a(n) is the number of strings of length n defined on {0,1,2,3} that contain at least two 2s or at least two 3s (or both).

Examples

			a(3)=20 since the strings are 220 (3 of this type), 221 (3 of this type), 223 (3 of this type), 330 (3 of this type), 331 (3 of this type), 332 (3 of this type), 222 and 333.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-36,56,-32).

Crossrefs

Cf. A000302, A007466.

Formula

E.g.f.: exp(4*x) - exp(2*x)*(1+x)^2.

a(n) = 4^n - A007466(n+1).

G.f.: 2*x^2/((1 - 2*x)^3*(1 - 4*x)). - Stefano Spezia, May 03 2025