A055838 T(2n+4,n), where T is the array in A055830.

5, 30, 162, 850, 4425, 22995, 119560, 622512, 3246750, 16963375, 88779900, 465386220, 2443204946, 12844119225, 67608235800, 356288599640, 1879625199825, 9925931817045, 52464942758250, 277546278287250

Offset

0,1

Links

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

Formula

Conjecture: 5*n*(n+3)*(n-1)*a(n) -2*(n-1)*(11*n+8)*(n+2)*a(n-1) -3*(3*n-1)*(3*n-2)*(n+1)*a(n-2)=0. - R. J. Mathar, Mar 13 2016

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+4, 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+4, 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+4, n) for n in (0..30)] # G. C. Greubel, Jan 21 2020

Crossrefs

Cf. A055830.

Sequence in context: A254944 A003731 A343362 * A318591 A094972 A084158

Adjacent sequences: A055835 A055836 A055837 * A055839 A055840 A055841

Keyword

nonn

Author

Clark Kimberling, May 28 2000

Status

approved