A027557 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..33.

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

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

MATHEMATICA

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

PROG