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A055838 T(2n+4,n), where T is the array in A055830. 2
5, 30, 162, 850, 4425, 22995, 119560, 622512, 3246750, 16963375, 88779900, 465386220, 2443204946, 12844119225, 67608235800, 356288599640, 1879625199825, 9925931817045, 52464942758250, 277546278287250 (list; graph; refs; listen; history; text; internal format)
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: A122995 A254944 A003731 * A318591 A094972 A084158

Adjacent sequences:  A055835 A055836 A055837 * A055839 A055840 A055841

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified July 12 23:28 EDT 2020. Contains 335669 sequences. (Running on oeis4.)