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A027028 a(n) = T(n,2n-4), T given by A027023.

%I A027028 #15 Mar 08 2023 04:08:49
%S A027028 1,1,5,17,53,161,477,1393,4033,11617,33365,95681,274209,785793,
%T A027028 2252509,6460433,18542169,53260481,153115765,440572993,1268830877,
%U A027028 3657435745,10551936125,30469329025,88056216233,254690980449
%N A027028 a(n) = T(n,2n-4), T given by A027023.
%H A027028 G. C. Greubel, <a href="/A027028/b027028.txt">Table of n, a(n) for n = 2..750</a>
%F A027028 Conjecture D-finite with recurrence -(n+2)*(n-6)*a(n) +3*(n+1)*(2*n-11)*a(n-1) -n*(7*n-31)*a(n-2) -2*(n-3)*(4*n-19)*a(n-3) +(5*n^2-38*n+84)*a(n-4) +(2*n-5)*(n-3)*a(n-5) +3*(n-3)*(n-4)*a(n-6)=0. - _R. J. Mathar_, Jun 24 2020
%F A027028 a(n) ~ 3^(n + 5/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Mar 08 2023
%p A027028 T:= proc(n, k) option remember;
%p A027028       if k<3 or k=2*n then 1
%p A027028     else add(T(n-1, k-j), j=1..3)
%p A027028       fi
%p A027028     end:
%p A027028 seq(T(n, 2*n-4), n=2..30); # _G. C. Greubel_, Nov 04 2019
%t A027028 T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]; Table[T[n, 2*n-4], {n, 2, 30}] (* _G. C. Greubel_, Nov 04 2019 *)
%o A027028 (Sage)
%o A027028 @CachedFunction
%o A027028 def T(n, k):
%o A027028     if (k<3 or k==2*n): return 1
%o A027028     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027028 [T(n, 2*n-4) for n in (2..30)] # _G. C. Greubel_, Nov 04 2019
%Y A027028 Cf. A027023.
%K A027028 nonn
%O A027028 2,3
%A A027028 _Clark Kimberling_