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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
OFFSET
0,1
LINKS
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved