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%I #14 May 15 2019 09:00:01
%S 0,0,0,0,1,2,7,16,40,92,209,468,1027,2242,4832,10360,22049,46694,
%T 98419,206588,432132,900980,1873297,3884904,8038295,16597478,34205700,
%U 70372728,144550977,296486538,607301551,1242406568,2538762208,5182207180
%N Number of (binary) bit strings of length n having at least one even length block of 0's followed by an even length block of 1's.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,-5,2).
%F G.f.: x^4/((1 - 2*x)*(1 - 3*x^2 - 2*x^3 + x^4)). [Corrected by _Georg Fischer_, May 15 2019]
%e a(6)=7 because of 000011, 001100, 001101, 001111, 010011, 100110, 110011.
%t CoefficientList[Series[x^4/((1 - 2 x) (1 - 3 x^2 - 2 x^3 + x^4)), {x, 0, 33}], x] (* _Georg Fischer_, May 15 2019 *)
%Y Cf. A065455, A065494, A065495.
%K nonn,easy
%O 0,6
%A _Len Smiley_, Nov 24 2001
%E Offset changed from 4 to 0 by _Georg Fischer_, May 15 2019