A384153 a(n) is the number of binary strings of length n whose shortest run of 1s is of length 1.
0, 1, 2, 4, 9, 20, 43, 91, 191, 398, 824, 1697, 3480, 7111, 14487, 29439, 59694, 120820, 244153, 492716, 993171, 1999923, 4023679, 8089182, 16251760, 32632321, 65490672, 131377999, 263452079, 528125695, 1058395038, 2120551916, 4247705401, 8506995748, 17034321659
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-5,3,-2).
Formula
G.f.: 1/(1-2*x) - (1-x)/(x*(1-2*x+x^2-x^3)).