A026744 a(n) = Sum_{j=0..floor(n/2)} T(n,j), T given by A026736.

1, 1, 3, 4, 12, 18, 51, 81, 220, 361, 952, 1595, 4118, 6999, 17787, 30548, 76696, 132766, 330148, 575054, 1418946, 2483812, 6089912, 10703456, 26104178, 46034722, 111769554, 197665364, 478085534, 847542518, 2043167075

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026736.

Programs

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/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, j], {j, 0, Floor[n/2]}], {n, 0, 35}] (* G. C. Greubel, Jul 22 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k==(n-2)/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, j) for j in (0..floor(n/2))) for n in (0..35)] # G. C. Greubel, Jul 22 2019