Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Jun 13 2015 00:49:07
%S 1,2,4,8,14,26,44,78,130,224,370,626,1028,1718,2810,4656,7594,12506,
%T 20356,33374,54242,88640,143906,234594,380548,619238,1003882,1631312,
%U 2643386,4291082,6950852,11274702,18258322,29598560
%N 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.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-2).
%F 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).
%F a(n) = 2*A000045(n+3) - 2^floor((n+2)/2) - 2^floor((n+1)/2). - _Max Alekseyev_, Jun 02 2005
%t LinearRecurrence[{1,3,-2,-2},{1,2,4,8},40] (* _Harvey P. Dale_, Feb 01 2012 *)
%o (PARI) a(n) = 2*fibonacci(n+3) - 2^((n+2)\2) - 2^((n+1)\2) /* _Max Alekseyev_ */
%K nonn
%O 0,2
%A _R. K. Guy_, _David Callan_