A027033 a(n) = T(n,2n-9), T given by A027023.

1, 3, 9, 31, 105, 355, 1197, 4011, 13329, 43883, 143105, 462391, 1481229, 4707743, 14856441, 46585671, 145253757, 450624055, 1391743825, 4281348119, 13124142489, 40105164499, 122213161617, 371496978671, 1126750503081

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<3 or k=2*n then 1
    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 05 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[T[n, 2*n-9], {n,5,30}] (* G. C. Greubel, Nov 05 2019 *)

Sage

@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    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 05 2019