A027070 a(n) = diagonal sum of right-justified array T given by A027052.

1, 1, 1, 4, 6, 12, 31, 73, 183, 476, 1248, 3322, 8943, 24271, 66355, 182538, 504824, 1402682, 3913585, 10959499, 30792445, 86775340, 245204312, 694603032, 1972115945, 5610955925, 15994866669, 45677496204, 130661330526, 374339736820, 1074025873959, 3085699969569, 8876601230175

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..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( add(T(n-k,2*n-3*k), k=0..n), n=0..35); # 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, 2*n-3*k], {k, 0, n}], {n,0,35}] (* 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,2*n-3*k) for k in (0..n)) for n in (0..35)] # G. C. Greubel, Nov 06 2019

Formula

a(n) = Sum_{k=0..n} A027052(n-k, 2*n-3*k). - Sean A. Irvine, Oct 22 2019

Extensions

More terms from Sean A. Irvine, Oct 22 2019