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A027060 a(n) = T(n,2n-4), T given by A027052.

%I A027060 #8 Nov 06 2019 04:27:17
%S A027060 1,1,3,11,35,107,319,935,2713,7825,22491,64523,184945,530001,1519151,
%T A027060 4356471,12501301,35901325,103188123,296844379,854701935,2463133311,
%U A027060 7104685935,20510632575,59262772629,171373598341,495968905267
%N A027060 a(n) = T(n,2n-4), T given by A027052.
%H A027060 G. C. Greubel, <a href="/A027060/b027060.txt">Table of n, a(n) for n = 2..750</a>
%p A027060 T:= proc(n, k) option remember;
%p A027060       if k<0 or k>2*n then 0
%p A027060     elif k=0 or k=2 or k=2*n then 1
%p A027060     elif k=1 then 0
%p A027060     else add(T(n-1, k-j), j=1..3)
%p A027060       fi
%p A027060     end:
%p A027060 seq( T(n,2*n-4), n=2..30); # _G. C. Greubel_, Nov 06 2019
%t A027060 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[T[n,2*n-4], {n,2,30}] (* _G. C. Greubel_, Nov 06 2019 *)
%o A027060 (Sage)
%o A027060 @CachedFunction
%o A027060 def T(n, k):
%o A027060     if (k<0 or k>2*n): return 0
%o A027060     elif (k==0 or k==2 or k==2*n): return 1
%o A027060     elif (k==1): return 0
%o A027060     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027060 [T(n,2*n-4) for n in (2..30)] # _G. C. Greubel_, Nov 06 2019
%K A027060 nonn
%O A027060 2,3
%A A027060 _Clark Kimberling_