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

1,3

Links

Table of n, a(n) for n=1..37.

Lars Blomberg, C# code for computing the terms of A284125

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

Example

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

Crossrefs

Cf. A284122.

Sequence in context: A080375 A136253 A266079 * A045678 A236002 A291406

Adjacent sequences: A284122 A284123 A284124 * A284126 A284127 A284128

Keyword

nonn

Author

Jeffrey Shallit, Mar 20 2017

Extensions

a(21)-a(37) from Lars Blomberg, Jun 06 2017

Status

approved