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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.
2

%I #15 Jun 07 2017 07:04:47

%S 0,0,2,4,12,26,52,98,178,316,556,972,1694,2950,5140,8968,15676,27460,

%T 48212,84844,149656,264578,468780,832344,1480860,2639730,4714066,

%U 8432938,15110070,27115448,48729252,87689374,157998112,285016412,514716578,930499110,1683776276

%N 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.

%H Lars Blomberg, <a href="/A284125/a284125.cs.txt">C# code for computing the terms of A284125</a>

%F 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

%e For n = 5 the 12 such strings are {00100,00101,00111,01000,01001,01101} and their binary complements.

%Y Cf. A284122.

%K nonn

%O 1,3

%A _Jeffrey Shallit_, Mar 20 2017

%E a(21)-a(37) from _Lars Blomberg_, Jun 06 2017