A027068 a(n) = Sum_{i=0..n} Sum_{j=i..2*i} A027052(i, j).

1, 2, 6, 16, 43, 120, 340, 972, 2793, 8050, 23256, 67324, 195275, 567448, 1651830, 4816328, 14064569, 41128626, 120425604, 353022920, 1035983443, 3043189688, 8947381566, 26328236756, 77531471737, 228475334594, 673725464150

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A027052. Partial sums of A027067.

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(add(T(k,j), j=k..2*k), k=0..n), n=0..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[Sum[T[i, j], {j, i, 2*i}], {i, 0, n}], {n,0,30}] (* 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(sum(T(k,j) for j in (k..2*k)) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

Extensions

Title corrected by Sean A. Irvine, Oct 22 2019