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G.f.: (1+x-2*x^2+2*x^3-sqrt(1-2*x-3*x^2+4*x^3-4*x^4))/(2*(1-x+x^2)).
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%I #17 Mar 09 2020 05:40:49

%S 0,1,1,1,2,3,7,14,33,73,174,407,987,2386,5877,14509,36210,90715,

%T 228863,579654,1475465,3768993,9664454,24857951,64133027,165900202,

%U 430242509,1118325365,2913106746,7603261427,19881409943,52076282638,136625968593,358989196793,944595607198,2488799333031,6565694568171

%N G.f.: (1+x-2*x^2+2*x^3-sqrt(1-2*x-3*x^2+4*x^3-4*x^4))/(2*(1-x+x^2)).

%H S. Kitaev and J. Remmel, <a href="http://arxiv.org/abs/1305.6970">The 1-box pattern on pattern avoiding permutations</a>, arXiv preprint arXiv:1305.6970 [math.CO], 2013. See Th. 8. also <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Kitaev/kitaev4.html">J. Int. Seq. 17 (2014) 14.3.3</a>

%F D-finite with recurrence: n*a(n) +3*(-n+1)*a(n-1) +6*a(n-2) +(5*n-24)*a(n-3) +(-11*n+51)*a(n-4) +2*(4*n-21)*a(n-5) +4*(-n+6)*a(n-6)=0. - _R. J. Mathar_, Jan 24 2018

%t CoefficientList[Series[(1+x-2x^2+2x^3-Sqrt[1-2x-3x^2+4x^3-4x^4])/(2(1-x+ x^2)),{x,0,40}],x] (* _Harvey P. Dale_, Apr 28 2016 *)

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Oct 01 2013