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

0,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A055830.

Sequence in context: A271560 A142040 A002648 * A243417 A367592 A163845

Adjacent sequences: A055837 A055838 A055839 * A055841 A055842 A055843

Keyword

nonn

Author

Clark Kimberling, May 28 2000

Extensions

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

Status

approved