A055840 T(2n+6,n), where T is the array in A055830.

13, 109, 707, 4184, 23720, 131389, 717927, 3889730, 20959485, 112529350, 602684170, 3222508015, 17211197614, 91855019053, 489986311295, 2612981923560, 13932202684630, 74280962031435, 396042187457445, 2111713236134025, 11260951929261216, 60058486994980518, 320362547860069042, 1709162928241695964

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+6, 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+3), 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+6, n) for n in (0..30)] # G. C. Greubel, Jan 21 2020

Extensions

Terms a(19) onward added by G. C. Greubel, Jan 21 2020