A027060 a(n) = T(n,2n-4), T given by A027052.

1, 1, 3, 11, 35, 107, 319, 935, 2713, 7825, 22491, 64523, 184945, 530001, 1519151, 4356471, 12501301, 35901325, 103188123, 296844379, 854701935, 2463133311, 7104685935, 20510632575, 59262772629, 171373598341, 495968905267

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..750

Programs

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( T(n,2*n-4), n=2..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[T[n,2*n-4], {n,2,30}] (* G. C. Greubel, Nov 06 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[T(n,2*n-4) for n in (2..30)] # G. C. Greubel, Nov 06 2019