cp's OEIS Frontend

A026755 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.

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