A027557 Number of 3-balanced strings of length n: let d(S)= #(1)'s in S - #(0)'s, then S is k-balanced if every substring T has -k<=d(T)<=k; here k=3.

1, 2, 4, 8, 14, 26, 44, 78, 130, 224, 370, 626, 1028, 1718, 2810, 4656, 7594, 12506, 20356, 33374, 54242, 88640, 143906, 234594, 380548, 619238, 1003882, 1631312, 2643386, 4291082, 6950852, 11274702, 18258322, 29598560

Offset: 0

Author

R. K. Guy, David Callan

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2).

Programs

Mathematica

LinearRecurrence[{1,3,-2,-2},{1,2,4,8},40] (* Harvey P. Dale, Feb 01 2012 *)

PARI

a(n) = 2*fibonacci(n+3) - 2^((n+2)\2) - 2^((n+1)\2) /* Max Alekseyev */

Formula

a(n) = a(n-1) + 3a(n-2) - 2a(n-3) - 2a(n-4); g.f. (1+x-x^2) / (1-x-x^2)(1-2x^2).

a(n) = 2*A000045(n+3) - 2^floor((n+2)/2) - 2^floor((n+1)/2). - Max Alekseyev, Jun 02 2005