%I #11 Nov 04 2019 19:38:45

%S 1,2,5,14,39,112,323,932,2693,7790,22565,65466,190243,553748,1614363,

%T 4713432,13780841,40343210,118243273,346937614,1018958151,2995407840,

%U 8812890391,25948662684,76457517949,225429675606,665069604713

%N a(n) = Sum_{k=0..n} T(n,n+k), T given by A027023.

%H G. C. Greubel, <a href="/A027035/b027035.txt">Table of n, a(n) for n = 0..1000</a>

%p T:= proc(n, k) option remember;

%p if k<3 or k=2*n then 1

%p else add(T(n-1, k-j), j=1..3)

%p fi

%p end:

%p seq(add(T(n, k), k=n..2*n), n=0..30); # _G. C. Greubel_, Nov 04 2019

%t T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k], {k,n,2*n}], {n,0,30}] (* _G. C. Greubel_, Nov 04 2019 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o if (k<3 or k==2*n): return 1

%o else: return sum(T(n-1, k-j) for j in (1..3))

%o [sum(T(n, k) for k in (n..2*n)) for n in (0..30)] # _G. C. Greubel_, Nov 04 2019

%K nonn

%O 0,2

%A _Clark Kimberling_