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%I #7 Oct 29 2019 21:09:58
%S 1,1,4,5,18,25,84,124,398,612,1901,3012,9126,14800,43968,72658,212417,
%T 356544,1028520,1749344,4989477,8583258,24244139,42121079,117973702,
%U 206754379,574811040,1015179978,2803969443,4986329826
%N a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.
%H G. C. Greubel, <a href="/A026755/b026755.txt">Table of n, a(n) for n = 0..1000</a>
%p A026747 := proc(n,k) option remember;
%p if k=0 or k = n then 1;
%p elif type(n,'even') and k <= n/2 then
%p procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
%p else
%p procname(n-1,k-1)+procname(n-1,k) ;
%p end if ;
%p end proc:
%p seq(add(A026747(n,k), k=0..floor(n/2)), n=0..30); # _G. C. Greubel_, Oct 29 2019
%t 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[Sum[T[n, k], Floor[n/2]], {n,0,30}] (* _G. C. Greubel_, Oct 29 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): 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, k) for k in (0..floor(n/2))) for n in (0..30)] # _G. C. Greubel_, Oct 29 2019
%Y Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026756, A026757.
%K nonn
%O 0,3
%A _Clark Kimberling_
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