%I A118898
%S A118898 0,0,0,0,1,2,5,12,28,62,136,294,628,1328,2787,5810,12043,24840,51016,
%T A118898 104380,212848,432732,877400,1774672,3581605,7213746,14502449,29106100,
%U A118898 58323844,116702074,233199000,465405058,927744428,1847359520,3674769991
%N A118898 Number of binary sequences of length n containing exactly one subsequence 
               0000.
%C A118898 Column 1 of A118897.
%F A118898 G.f.=z^4/(1-z-z^2-z^3-z^4)^2.
%F A118898 Contribution from Bobby Milazzo [bobbym] (mpopyft(AT)lycos.com), Aug 
               30 2009: (Start)
%F A118898 a(1)=0,a(2)=0,a(3)=0,a(4)=1,a(5)=2,a(6)=5,a(7)=12,a(8)=28
%F A118898 a(n)=2a(n-1)+a(n-2)-a(n-4)-4a(n-5)-3a(n-6)-2a(n-7)-a(n-8) (End)
%e A118898 a(6)=5 because we have 000010,000011,010000,100001 and 110000.
%e A118898 sage: taylor( mul(x/(1-x-x^2-x^3-x^4)^2 for i in xrange(1,2)),x,0,31)# 
               solution>> x + 2*x^2 + 5*x^3 + 12*x^4 + 28*x^5 + 62*x^6 +...+ 465405058*x^28 
               + 927744428*x^29 + 1847359520*x^30 + 3674769991*x^31+etc... and if 
               sage: taylor( mul(x^4/(1-x-x^2-x^3-x^4)^2 for i in xrange(1,2)),x,
               0,34)#(Emeric Deutsch) then solution: x^4 + 2*x^5 + 5*x^6 + 12*x^7 
               + 28*x^8 + 62*x^9 +...+ 465405058*x^31 + 927744428*x^32 + 1847359520*x^33 
               + 3674769991*x^34+etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 02 2009]
%p A118898 g:=z^4/(1-z-z^2-z^3-z^4)^2: gser:=series(g,z=0,40): seq(coeff(gser,z,
               n),n=0..37);
%t A118898 Contribution from Bobby Milazzo [bobbym] (mpopyft(AT)lycos.com), Aug 
               30 2009: (Start)
%t A118898 With Mathematica 7.01
%t A118898 RecurrenceTable[{a[1]==0,a[2]==0,a[3]==0,a[4]==1,a[5]==2,a[6]==5,
%t A118898 a[7]==12,a[8]==28,a[n]==2a[n-1]+a[n-2]-a[n-4]-4a[n-5]
%t A118898 -3a[n-6]-2a[n-7]-a[n-8]},a,{n,9,50}] (End)
%o A118898 (Other) sage: taylor( mul(x/(1-x-x^2-x^3-x^4)^2 for i in xrange(1,2)),
               x,0,31)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 
               02 2009]
%Y A118898 Cf. A118897, A000078.
%Y A118898 Sequence in context: A128096 A018010 A026710 this_sequence A111586 A006979 
               A019301
%Y A118898 Adjacent sequences: A118895 A118896 A118897 this_sequence A118899 A118900 
               A118901
%K A118898 nonn
%O A118898 0,6
%A A118898 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 04 2006