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

1, 1, 4, 5, 18, 25, 84, 124, 398, 612, 1901, 3012, 9126, 14800, 43968, 72658, 212417, 356544, 1028520, 1749344, 4989477, 8583258, 24244139, 42121079, 117973702, 206754379, 574811040, 1015179978, 2803969443, 4986329826

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026756, A026757.

Programs

Maple

A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(add(A026747(n,k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019

Mathematica

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 *)

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[sum(T(n, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 29 2019