A284125 Number of binary strings w of length n for which s, the longest proper suffix of w that appears at least twice in w, is of length 2.
0, 0, 2, 4, 12, 26, 52, 98, 178, 316, 556, 972, 1694, 2950, 5140, 8968, 15676, 27460, 48212, 84844, 149656, 264578, 468780, 832344, 1480860, 2639730, 4714066, 8432938, 15110070, 27115448, 48729252, 87689374, 157998112, 285016412, 514716578, 930499110, 1683776276
Offset: 1
Keywords
Examples
For n = 5 the 12 such strings are {00100,00101,00111,01000,01001,01101} and their binary complements.
Links
- Lars Blomberg, C# code for computing the terms of A284125
Crossrefs
Cf. A284122.
Formula
G.f.: 2*x^3*(1 + x^2)*(1 - 4*x + 6*x^2 - 5*x^3 + x^4 + 2*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^2*(1 - x - x^2)*(1 - 2*x + x^2 - x^3)*(1 - x - x^2 - x^3)) (conjectured). - Colin Barker, Jun 07 2017
Extensions
a(21)-a(37) from Lars Blomberg, Jun 06 2017