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A026753 a(n) = T(n, floor(n/2)), T given by A026747.

%I A026753 #9 Oct 29 2019 21:10:10
%S A026753 1,1,3,4,11,17,44,74,184,327,790,1461,3452,6584,15278,29879,68290,
%T A026753 136391,307696,625731,1395696,2883357,6367199,13338421,29193025,
%U A026753 61920497,134442102,288368511,621609060,1346873365,2884432810
%N A026753 a(n) = T(n, floor(n/2)), T given by A026747.
%H A026753 G. C. Greubel, <a href="/A026753/b026753.txt">Table of n, a(n) for n = 0..1000</a>
%p A026753 A026747 := proc(n,k) option remember;
%p A026753    if k=0 or k = n then 1;
%p A026753    elif type(n,'even') and k <= n/2 then
%p A026753         procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p A026753    else
%p A026753        procname(n-1,k-1)+procname(n-1,k) ;
%p A026753    end if ;
%p A026753 end proc:
%p A026753 seq(A026747(n,floor(n/2)), n=0..30); # _G. C. Greubel_, Oct 29 2019
%t A026753 T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && 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] ]]; Table[T[n, Floor[n/2]], {n,0,30}] (* _G. C. Greubel_, Oct 29 2019 *)
%o A026753 (Sage)
%o A026753 @CachedFunction
%o A026753 def T(n, k):
%o A026753     if (k==0 or k==n): return 1
%o A026753     elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
%o A026753     else: return T(n-1,k-1) + T(n-1,k)
%o A026753 [T(n, floor(n/2)) for n in (0..30)] # _G. C. Greubel_, Oct 29 2019
%Y A026753 Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026754, A026755, A026756, A026757.
%K A026753 nonn
%O A026753 0,3
%A A026753 _Clark Kimberling_