A055839 T(2n+5,n), where T is the array in A055830.

8, 58, 344, 1918, 10415, 55837, 297374, 1578160, 8359845, 44244825, 234094080, 1238598580, 6555004313, 34703385031, 183805639190, 973982775784, 5163655102685, 27389161216395, 145349642782140, 771718011707550

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A055830.

Programs

Maple

with(combinat);
T:= proc(n, k) option remember;
      if k<0 or k>n then 0
    elif k=0 then fibonacci(n+1)
    elif n=1 and k=1 then 0
    else T(n-1, k-1) + T(n-1, k) + T(n-2, k)
      fi; end:
seq(T(2*n+5, n), n=0..30); # G. C. Greubel, Jan 21 2020

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==0, Fibonacci[n+1], If[n==1 && k==1, 0, T[n-1, k-1] + T[n-1, k] + T[n-2, k]]]]; Table[T[2*n+5, n], {n,0,30}] (* G. C. Greubel, Jan 21 2020 *)

Sage

@CachedFunction
def T(n, k):
    if (k<0 and k>n): return 0
    elif (k==0): return fibonacci(n+1)
    elif (n==1 and k==1): return 0
    else: return T(n-1, k-1) + T(n-1, k) + T(n-2, k)
[T(2*n+5, n) for n in (0..30)] # G. C. Greubel, Jan 21 2020