A384154 a(n) is the number of binary strings of length n whose shortest run of 1s is of length 2.

0, 0, 1, 2, 3, 5, 10, 20, 38, 70, 128, 234, 427, 776, 1404, 2531, 4550, 8161, 14608, 26099, 46550, 82901, 147441, 261913, 464759, 823902, 1459287, 2582615, 4567357, 8072082, 14257631, 25169443, 44410452, 78325112, 138082349, 243339192, 428683436, 754961473

Offset: 0

Author

Félix Balado, May 20 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-2,-1,1,-1).

Crossrefs

Cf. A000100, A384153.

Programs

Mathematica

LinearRecurrence[{4,-6,5,-2,-1,1,-1},{0,0,1,2,3,5,10},40] (* Harvey P. Dale, Jun 24 2025 *)

Formula

G.f.: x^2 * (1 - x)^2/(((1 - x)^2 - x^3) * ((1 - x)^2 - x^4)).