%I #12 Dec 22 2021 07:04:16
%S 1,1,1,2,5,8,16,28,65,111,251,436,1016,1763,4117,7176,16913,29521,
%T 69865,122182,290455,508595,1212905,2126312,5085224,8923136,21389824,
%U 37563930,90226449,158563368,381519416,670893296,1616684241,2844444761
%N a(n) = T(n, floor(n/2)), T given by A026519.
%H G. C. Greubel, <a href="/A026530/b026530.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = A026519(n, floor(n/2)).
%t T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
%t a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, T[n, Floor[n/2]] ];
%t Table[a[n], {n, 0, 40}] (* _G. C. Greubel_, Dec 21 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n,k): # T = A026519
%o if (k<0 or k>2*n): return 0
%o elif (k==0 or k==2*n): return 1
%o elif (k==1 or k==2*n-1): return (n+1)//2
%o elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o [T(n, n//2) for n in (0..40)] # _G. C. Greubel_, Dec 21 2021
%Y Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026531, A026532, A026533, A026534, A027262, A027263, A027264, A027265, A027266.
%K nonn
%O 0,4
%A _Clark Kimberling_