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

0,6

Links

Table of n, a(n) for n=0..33.

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A065455, A065494, A065495.

Sequence in context: A041887 A129441 A093971 * A131727 A320236 A073371

Adjacent sequences: A065494 A065495 A065496 * A065498 A065499 A065500

Keyword

nonn,easy

Author

Len Smiley, Nov 24 2001

Extensions

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

Status

approved