A027035 a(n) = Sum_{k=0..n} T(n,n+k), T given by A027023.

1, 2, 5, 14, 39, 112, 323, 932, 2693, 7790, 22565, 65466, 190243, 553748, 1614363, 4713432, 13780841, 40343210, 118243273, 346937614, 1018958151, 2995407840, 8812890391, 25948662684, 76457517949, 225429675606, 665069604713

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

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(add(T(n, k), k=n..2*n), n=0..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,2*n}], {n,0,30}] (* 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..2*n)) for n in (0..30)] # G. C. Greubel, Nov 04 2019