%I A125513
%S A125513 2,4,8,15,26,48,89,165,305,561,1034,1908,3521,6496,11982,22101,40770,
%T A125513 75210,138741,255934,472117,870911,1606567,2963628,5466988,10084919,
%U A125513 18603592,34317946,63306130,116780470,215424285,397391986,733066807
%N A125513 a(n) is the number of binary strings of length n such that no subsequence 
               of length 5 or less contains 4 or more ones.
%F A125513 a(n) = a(n-1) + a(n-2) + a(n-4) + 2a(n-5) - a(n-7) - a(n-10).
%F A125513 G.f.: x*(2+2*x+2*x^2+3*x^3+x^4-x^5-x^6-x^7-x^8-x^9)/(1-x-x^2-x^4-2*x^5+x^7+x^ 
               10) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
%Y A125513 This sequence is similar to the sequences A118647 (where no substring 
               of length 4 contains 3 or more ones), because the number of ones 
               we are checking for is one less than the length of a substring. It 
               is also similar to A120118 (where no substring of length 5 contains 
               3 or more ones.).
%Y A125513 Sequence in context: A133551 A114226 A003241 this_sequence A054174 A001523 
               A000126
%Y A125513 Adjacent sequences: A125510 A125511 A125512 this_sequence A125514 A125515 
               A125516
%K A125513 nonn
%O A125513 1,1
%A A125513 Tanya Khovanova (tanyakh(AT)yahoo.com), Dec 28 2006
%E A125513 G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, 
               Sep 16 2009.