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%I #10 Jan 21 2020 10:08:46
%S 8,58,344,1918,10415,55837,297374,1578160,8359845,44244825,234094080,
%T 1238598580,6555004313,34703385031,183805639190,973982775784,
%U 5163655102685,27389161216395,145349642782140,771718011707550
%N T(2n+5,n), where T is the array in A055830.
%H G. C. Greubel, <a href="/A055839/b055839.txt">Table of n, a(n) for n = 0..500</a>
%p with(combinat);
%p T:= proc(n, k) option remember;
%p if k<0 or k>n then 0
%p elif k=0 then fibonacci(n+1)
%p elif n=1 and k=1 then 0
%p else T(n-1, k-1) + T(n-1, k) + T(n-2, k)
%p fi; end:
%p seq(T(2*n+5, n), n=0..30); # _G. C. Greubel_, Jan 21 2020
%t 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+5, n], {n,0,30}] (* _G. C. Greubel_, Jan 21 2020 *)
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k<0 and k>n): return 0
%o elif (k==0): return fibonacci(n+1)
%o elif (n==1 and k==1): return 0
%o else: return T(n-1, k-1) + T(n-1, k) + T(n-2, k)
%o [T(2*n+5, n) for n in (0..30)] # _G. C. Greubel_, Jan 21 2020
%Y Cf. A055830.
%K nonn
%O 0,1
%A _Clark Kimberling_, May 28 2000
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