|
%I #5 May 14 2017 11:30:08
%S 2,4,8,15,26,48,89,165,305,561,1034,1908,3521,6496,11982,22101,40770,
%T 75210,138741,255934,472117,870911,1606567,2963628,5466988,10084919,
%U 18603592,34317946,63306130,116780470,215424285,397391986,733066807
%N 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.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 1, 2, 0, -1, 0, 0, -1).
%F a(n) = a(n-1) + a(n-2) + a(n-4) + 2a(n-5) - a(n-7) - a(n-10).
%F 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 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.).
%K nonn
%O 1,1
%A _Tanya Khovanova_, Dec 28 2006
%E G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
|
