A027077 a(n) = Sum_{k=n+1..2*n} T(n,k), T given by A027052.

1, 3, 8, 24, 71, 209, 612, 1784, 5189, 15081, 43838, 127528, 371395, 1082951, 3161866, 9243400, 27055153, 79280601, 232567194, 682905120, 2007104343, 5904004451, 17380510458, 51202600920, 150942696637, 445247984543

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

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( add(T(n,k), k=n+1..2*n), n=1..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[Sum[T[n, k], {k, n+1, 2*n}], {n, 1, 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))
[sum(T(n,k) for k in (n+1..2*n)) for n in (1..30)] # G. C. Greubel, Nov 06 2019

Extensions

Offset changed by G. C. Greubel, Nov 06 2019