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A026775 a(n) = T(n, floor(n/2)), T given by A026769.

%I A026775 #7 Nov 01 2019 22:23:13
%S A026775 1,1,2,4,7,17,28,76,120,352,538,1674,2493,8129,11854,40156,57558,
%T A026775 201236,284392,1020922,1426038,5234660,7241356,27089726,37173304,
%U A026775 141335846,192638992,742712598,1006564439,3927908193,5297715628
%N A026775 a(n) = T(n, floor(n/2)), T given by A026769.
%H A026775 G. C. Greubel, <a href="/A026775/b026775.txt">Table of n, a(n) for n = 0..1000</a>
%p A026775 T:= proc(n,k) option remember;
%p A026775    if n<0 then 0;
%p A026775    elif k=0 or k=n then 1;
%p A026775    elif n=2 and k=1 then 2;
%p A026775    elif k <= (n-1)/2 then
%p A026775         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026775    else
%p A026775        procname(n-1,k-1)+procname(n-1,k) ;
%p A026775    end if ;
%p A026775 end proc;
%p A026775 seq(T(n, floor(n/2)), n=0..30); # _G. C. Greubel_, Nov 01 2019
%t A026775 T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[k<=(n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]]; Table[T[n, Floor[n/2]], {n,0,30}] (* _G. C. Greubel_, Nov 01 2019 *)
%o A026775 (Sage)
%o A026775 @CachedFunction
%o A026775 def T(n, k):
%o A026775     if (k==0 or k==n): return 1
%o A026775     elif (n==2 and k==1): return 2
%o A026775     elif (k<=(n-1)/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026775     else: return T(n-1,k-1) + T(n-1,k)
%o A026775 [T(n, floor(n/2)) for n in (0..30)] # _G. C. Greubel_, Nov 01 2019
%Y A026775 Cf. A026769, A026770, A026771, A026772, A026773, A026774, A026776, A026777, A026778, A026779.
%K A026775 nonn
%O A026775 0,3
%A A026775 _Clark Kimberling_