A384497 a(n) is the number of binary strings of length n which contain exactly one run of 1s of even length.

0, 0, 1, 2, 6, 12, 28, 56, 119, 236, 479, 940, 1859, 3612, 7028, 13538, 26051, 49820, 95098, 180774, 342944, 648648, 1224517, 2306338, 4336449, 8138516, 15250965, 28535528, 53320792, 99504804, 185474501, 345332950, 642310142, 1193510160, 2215702468, 4109801864

Offset: 0

Author

Félix Balado, May 31 2025

Keywords

• nonn
• easy

Examples

			a(3)=2 because of the strings 011 and 110.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-2,4,-1).

Crossrefs

Cf. A029907.

Programs

Mathematica

CoefficientList[Series[((1 - x^2) * x^2)/(1 - x - 2 * x^2 + x^3)^2,{x,0,35}],x] (* Stefano Spezia, Jun 02 2025 *)

Formula

G.f.: ((1 - x^2) * x^2)/(1 - x - 2 * x^2 + x^3)^2.