%I
%S 1,1,2,7,8,26,32,85,128,292,512,1079,2048,4174,8192,16489,32768,65672,
%T 131072,262315,524288,1048786,2097152,4194557,8388608,16777516,
%U 33554432,67109215,134217728,268435862,536870912,1073742289,2147483648,4294967824,8589934592
%N Number of length n binary words that contain an even number of 0's or exactly two 1's.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,6,3,6,1,2).
%F G.f.: (1 x  3*x^2 + 6*x^3  3*x^4  2*x^5  3*x^6 + x^7)/( (1  2*x)*(1  x^2)^3 ).
%F a(n) = (2^(1+n))/4 for n even; a(n) = (2^(1+n)2*n+2*n^2)/4 for n odd.  _Colin Barker_, Jan 23 2014
%e a(3)=7 because we have: 001, 010, 011, 100, 101, 110, 111.
%t nn=30;CoefficientList[Series[(1x3*x^2+6*x^33*x^42*x^53*x^6+x^7)/ ((12*x)*(1x^2)^3),{x,0,nn}],x]
%Y Cf. A161680 (words containing exactly two 1's), A011782 (words containing an even number of 0's), A000384 (words containing an even number of 0's and exactly 2 1's).
%K nonn,easy
%O 0,3
%A _Geoffrey Critzer_, Jan 21 2014
%E More terms from _Colin Barker_, Jan 23 2014
