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A027033 a(n) = T(n,2n-9), T given by A027023.

%I A027033 #7 Nov 05 2019 12:22:48
%S A027033 1,3,9,31,105,355,1197,4011,13329,43883,143105,462391,1481229,4707743,
%T A027033 14856441,46585671,145253757,450624055,1391743825,4281348119,
%U A027033 13124142489,40105164499,122213161617,371496978671,1126750503081
%N A027033 a(n) = T(n,2n-9), T given by A027023.
%H A027033 G. C. Greubel, <a href="/A027033/b027033.txt">Table of n, a(n) for n = 5..750</a>
%p A027033 T:= proc(n, k) option remember;
%p A027033       if k<3 or k=2*n then 1
%p A027033     else add(T(n-1, k-j), j=1..3)
%p A027033       fi
%p A027033     end:
%p A027033 seq(T(n,2*n-9), n=5..30); # _G. C. Greubel_, Nov 05 2019
%t A027033 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[T[n, 2*n-9], {n,5,30}] (* _G. C. Greubel_, Nov 05 2019 *)
%o A027033 (Sage)
%o A027033 @CachedFunction
%o A027033 def T(n, k):
%o A027033     if (k<3 or k==2*n): return 1
%o A027033     else: return sum(T(n-1, k-j) for j in (1..3))
%o A027033 [T(n, 2*n-9) for n in (5..30)] # _G. C. Greubel_, Nov 05 2019
%K A027033 nonn
%O A027033 5,2
%A A027033 _Clark Kimberling_