A027057 a(n) = (1/2) * A027052(n, 2n-1).

1, 2, 4, 9, 21, 51, 128, 329, 861, 2285, 6132, 16606, 45313, 124446, 343680, 953753, 2658133, 7436541, 20875972, 58783892, 165989825, 469903672, 1333359488, 3791535934, 10802911297, 30836181436, 88169413364, 252500533673, 724182805389, 2079862921763, 5981150599872

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-1)/2, 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-1]/2, {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-1)/2 for n in (2..30)] # G. C. Greubel, Nov 06 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019