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%I #14 Jul 30 2015 22:41:36
%S 1,2,4,8,16,32,62,122,232,450,846,1622,3026,5748,10664,20106,37144,
%T 69608,128164,238984,438826,814874,1492908,2762562,5051602,9320014,
%U 17014950,31311964,57084732,104819474,190865620,349797128,636274832
%N Number of 5-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=5.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 5, -4, -6, 3).
%F a_n = a_{n-1} + 5a_{n-2} - 4a_{n-3} - 6a_{n-4} + 3a_{n-5}.
%F G.f. (1+x-3x^2-2x^3+2x^4-x^5) / (1-x-2x^2+x^3)(1-3x^2). - _David Callan_, Jul 22 2008
%t Join[{1},LinearRecurrence[{1,5,-4,-6,3},{2,4,8,16,32},40]] (* _Harvey P. Dale_, May 01 2013 *)
%K nonn
%O 0,2
%A _R. K. Guy_, _David Callan_
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