A027065 a(n) = A027052(n, 2n-9).

0, 2, 6, 20, 68, 230, 776, 2604, 8670, 28606, 93494, 302748, 971810, 3094486, 9782092, 30721056, 95919714, 297938906, 921183940, 2836545972, 8702745304, 26614653494, 81159163058, 246855070144, 749123740876, 2268700324802

Offset: 5

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 5..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-9), n=5..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-9], {n,5,30}] (* 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-9) for n in (5..30)] # G. C. Greubel, Nov 06 2019