A065497 Number of (binary) bit strings of length n having at least one even length block of 0's followed by an even length block of 1's.

0, 0, 0, 0, 1, 2, 7, 16, 40, 92, 209, 468, 1027, 2242, 4832, 10360, 22049, 46694, 98419, 206588, 432132, 900980, 1873297, 3884904, 8038295, 16597478, 34205700, 70372728, 144550977, 296486538, 607301551, 1242406568, 2538762208, 5182207180

Offset: 0

Author

Len Smiley, Nov 24 2001

Keywords

• nonn
• easy

Examples

			a(6)=7 because of 000011, 001100, 001101, 001111, 010011, 100110, 110011.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-5,2).

Crossrefs

Cf. A065455, A065494, A065495.

Programs

Mathematica

CoefficientList[Series[x^4/((1 - 2 x) (1 - 3 x^2 - 2 x^3 + x^4)), {x, 0, 33}], x] (* Georg Fischer, May 15 2019 *)

Formula

G.f.: x^4/((1 - 2*x)*(1 - 3*x^2 - 2*x^3 + x^4)). [Corrected by Georg Fischer, May 15 2019]

Extensions

Offset changed from 4 to 0 by Georg Fischer, May 15 2019