A026768 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758.

1, 1, 2, 3, 6, 9, 16, 29, 46, 82, 145, 237, 421, 737, 1228, 2171, 3788, 6388, 11253, 19617, 33344, 58597, 102141, 174571, 306294, 533976, 916309, 1605975, 2800260, 4820020, 8441365, 14721208, 25399974, 44458045, 77542951

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026758, A026759, A026760, A026761, A026762, A026763, A026764, A026765, A026766, A026767.

Programs

Maple

T:= proc(n,k) option remember;
   if n<0 then 0;
   elif k=0 or k = n then 1;
   elif type(n,'odd') and k <= (n-1)/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(T(n-k,k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 31 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && 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[Sum[T[n-k,k], {k,0,Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Oct 31 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (mod(n,2)==1 and k<=(n-1)/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, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 31 2019