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
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
EXTENSIONS
Terms a(19) onward added by G. C. Greubel, Jan 21 2020
STATUS
approved