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%I #17 Jan 30 2020 22:07:14
%S 1,1,2,6,12,32,80,200,520,1336,3472,9072,23744,62432,164544,434688,
%T 1150944,3052768,8110784,21581120,57498496,153378048,409583616,
%U 1094848768,2929288960,7843943680,21020501504,56371941888,151276652544
%N Expansion of (1+x)/sqrt(1-4x^2-8x^3-4x^4).
%C Binomial transform is A101500. Binomial transform of A102882.
%C Apparently the number of grand Motzkin paths of length n that avoid FF (double flat steps). - _David Scambler_, Jul 04 2013
%H Vincenzo Librandi, <a href="/A102881/b102881.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (1+x)/sqrt((1-2x-2x^2)(1+2x+2x^2)).
%F D-finite with recurrence: n*a(n) +(n-2)*a(n-1) +4*(-n+1)*a(n-2) +12*(-n+2)*a(n-3) +12*(-n+3)*a(n-4) +4*(-n+4)*a(n-5)=0. - _R. J. Mathar_, Nov 16 2012
%F D-finite with recurrence (of order 4): (n-1)*n*a(n) = 4*(n-1)^2*a(n-2) + 4*(n-2)*(2*n-1)*a(n-3) + 4*(n-3)*n*a(n-4). - _Vaclav Kotesovec_, Feb 08 2014
%F a(n) ~ sqrt(54+30*sqrt(3)) * (1+sqrt(3))^n / (12 * sqrt(Pi*n)). - _Vaclav Kotesovec_, Feb 08 2014
%t CoefficientList[Series[(1+x)/Sqrt[1-4*x^2-8*x^3-4*x^4], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 08 2014 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jan 15 2005
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