A055837 T(2n+3,n), where T is the array in A055830.

3, 15, 73, 361, 1806, 9122, 46425, 237721, 1223365, 6321965, 32784830, 170528190, 889291352, 4648068192, 24342384337, 127707864849, 671047979300, 3531026714720, 18603737992455, 98129545962855, 518149580437560

Offset

0,1

Links

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

Formula

Conjecture: 5*n*(n+2)*(11*n-4)*a(n) +(-242*n^3-330*n^2+29*n+42)*a(n-1) -3*(3*n-1)*(11*n+7)*(3*n-2)*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+3, 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 or 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+3, n) for n in (0..30)] # G. C. Greubel, Jan 21 2020

Crossrefs

Cf. A055830.

Sequence in context: A145839 A232289 A370480 * A124543 A007142 A357222

Adjacent sequences: A055834 A055835 A055836 * A055838 A055839 A055840

Keyword

nonn

Author

Clark Kimberling, May 28 2000

Status

approved