%I A066067
%S A066067 1,2,3,6,10,18,29,49,78,128,203,329,523,844,1347,2172,3480,5614,9023,
%T A066067 14567,23466,37910,61165
%N A066067 Number of binary strings u of any length with property that length(u) 
               + number of 0's in u <= n (only one of a string and its reversal 
               are counted).
%C A066067 If 0 is replaced by 2 (as in A007931) "length + 0-bits" is simply the 
               total of ternary digits (e.g. 3 for 21 instead of 01).
%F A066067 G.f.: x(-x^7-x^4+3x^3-2x^2-x+1)/[(1-x-x^2)(1-x^2-x^4)(1-x)^2].
%e A066067 a(3) = 3: 0 01 111 (e.g. 01: length 2 + 1 zero = 3)
%e A066067 a(4) = 6: 0 01 00 011 101 1111
%e A066067 a(5) =10: 0 01 00 011 101 001 010 0111 1011 11111
%Y A066067 If reversals are counted as distinct then we obtain A000126.
%Y A066067 A007931 (binary strings represented by ternary numbers),
%Y A066067 Cf. A035615 (binary "same game").
%Y A066067 Sequence in context: A081028 A065441 A075531 this_sequence A121364 A102702 
               A060945
%Y A066067 Adjacent sequences: A066064 A066065 A066066 this_sequence A066068 A066069 
               A066070
%K A066067 nonn
%O A066067 1,2
%A A066067 Frank.Ellermann(AT)t-online.de, Dec 02 2001