A027045 a(n) = Sum_{k=n+1..2*n} T(n, k), T given by A027023.

1, 4, 11, 34, 103, 306, 901, 2636, 7685, 22372, 65111, 189590, 552547, 1612154, 4709369, 13773368, 40329465, 118217992, 346891115, 1018872626, 2995250535, 8812601062, 25948130525, 76456539156, 225427875325, 665066293480

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A027023.

Programs

Magma

function T(n,k)
  if k lt 3 or k eq 2*n then return 1;
  else return (&+[T(n-1,k-j): j in [1..3]]);
  end if; return T; end function;
[(&+[T(n,k): k in [n+1..2*n]]): n in [1..15]]; // G. C. Greubel, Nov 20 2019

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(add(T(n, k), k=n+1..2*n), n=1..30); # G. C. Greubel, Nov 04 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[T[n,k], {k,n+1,2*n}], {n,30}] (* G. C. Greubel, Nov 04 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))
[sum(T(n, k) for k in (n+1..2*n)) for n in (1..30)] # G. C. Greubel, Nov 04 2019

Extensions

Offset changed by G. C. Greubel, Nov 04 2019