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A026786 a(n) = T(n, floor(n/2)), T given by A026780.

%I A026786 #8 Nov 03 2019 02:14:47
%S A026786 1,1,3,5,12,24,53,117,246,580,1178,2916,5768,14834,28731,76221,145108,
%T A026786 395048,741392,2063104,3825418,10847078,19907156,57373672,104370554,
%U A026786 305110106,550816506,1630489090,2924018194,8751851866
%N A026786 a(n) = T(n, floor(n/2)), T given by A026780.
%H A026786 G. C. Greubel, <a href="/A026786/b026786.txt">Table of n, a(n) for n = 0..1000</a>
%p A026786 T:= proc(n,k) option remember;
%p A026786     if n<0 then 0;
%p A026786     elif k=0 or k =n then 1;
%p A026786     elif k <= n/2 then
%p A026786         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026786     else
%p A026786         procname(n-1,k-1)+procname(n-1,k) ;
%p A026786     fi ;
%p A026786 end proc:
%p A026786 seq(T(n, floor(n/2)), n=0..30); # _G. C. Greubel_, Nov 02 2019
%t A026786 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[k<=n/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 A026786 Table[T[n, Floor[n/2]], {n,0,30}] (* _G. C. Greubel_, Nov 02 2019 *)
%o A026786 (Sage)
%o A026786 @CachedFunction
%o A026786 def T(n, k):
%o A026786     if (n<0): return 0
%o A026786     elif (k==0 or k==n): return 1
%o A026786     elif (k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026786     else: return T(n-1,k-1) + T(n-1,k)
%o A026786 [T(n, floor(n/2)) for n in (0..30)] # _G. C. Greubel_, Nov 02 2019
%Y A026786 Cf. A026780, A026781, A026782, A026783, A026784, A026785, A026787, A026788, A026789, A026790.
%K A026786 nonn
%O A026786 0,3
%A A026786 _Clark Kimberling_