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%I #8 Jul 23 2019 08:51:51
%S 1,1,3,4,12,18,51,81,220,361,952,1595,4118,6999,17787,30548,76696,
%T 132766,330148,575054,1418946,2483812,6089912,10703456,26104178,
%U 46034722,111769554,197665364,478085534,847542518,2043167075
%N a(n) = Sum_{j=0..floor(n/2)} T(n,j), T given by A026736.
%H G. C. Greubel, <a href="/A026744/b026744.txt">Table of n, a(n) for n = 0..1000</a>
%t T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]];
%t Table[Sum[T[n, j], {j, 0, Floor[n/2]}], {n, 0, 35}] (* _G. C. Greubel_, Jul 22 2019 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k==0 or k==n): return 1
%o elif (mod(n,2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
%o else: return T(n-1, k-1) + T(n-1, k)
%o [sum(T(n, j) for j in (0..floor(n/2))) for n in (0..35)] # _G. C. Greubel_, Jul 22 2019
%Y Cf. A026736.
%K nonn
%O 0,3
%A _Clark Kimberling_
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