A026789 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026780.

1, 3, 8, 19, 45, 103, 239, 545, 1262, 2887, 6700, 15397, 35848, 82757, 193320, 448175, 1050217, 2443963, 5743267, 13410053, 31593029, 73984575, 174689181, 410141597, 970289011, 2283205051, 5410611863, 12756825609, 30274963923

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Partial sums of A026787.

Cf. A026780, A026781, A026782, A026783, A026784, A026785, A026786, A026788, A026790.

Programs

Maple

T:= proc(n,k) option remember;
    if n<0 then 0;
    elif k=0 or k =n then 1;
    elif 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) ;
    fi ;
end proc:
seq( add(add(T(j,k), k=0..n), j=0..n), n=0..30); # G. C. Greubel, Nov 02 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[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[j, k], {k, 0, n}, {j, 0, n}], {n,0,30}] (* G. C. Greubel, Nov 02 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (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( sum( T(j,k) for k in (0..n)) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 02 2019