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%I #24 Jul 22 2019 20:45:30
%S 0,1,0,2,1,3,4,5,10,11,21,27,43,64,92,144,205,316,462,693,1035,1532,
%T 2301,3406,5099,7581,11303,16855,25088,37432,55728,83097,123800,
%U 184490,274969,409683,610628,909845,1355970,2020635,3011157,4487395,6686979
%N Expansion of x/(1 - 2*x^2 - x^3 + x^4).
%C a(n) is the number of compositions of n+2 such that: i) the first part is odd, ii) the last part is even, and iii) no two consecutive parts have the same parity. - _Geoffrey Critzer_, Mar 04 2012
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1).
%e a(7) = 5 because there are 5 such compositions of the integer 9: 1+8, 7+2, 3+6, 5+4, 1+2+1+2+1+2. - _Geoffrey Critzer_, Mar 04 2012
%t nn = 44; a = x/(1 - x^2); b = x^2/(1 - x^2); Drop[ CoefficientList[Series[1/(1 - a b), {x, 0, nn}], x], 2] (* _Geoffrey Critzer_, Mar 04 2012 *)
%t CoefficientList[Series[x/(1-2x^2-x^3+x^4),{x,0,50}],x] (* _Harvey P. Dale_, Jul 17 2019 *)
%Y Cf. A006054, A006053.
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, Sep 16 2006
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