This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A055840 #10 Jan 21 2020 10:08:53
%S A055840 13,109,707,4184,23720,131389,717927,3889730,20959485,112529350,
%T A055840 602684170,3222508015,17211197614,91855019053,489986311295,
%U A055840 2612981923560,13932202684630,74280962031435,396042187457445,2111713236134025,11260951929261216,60058486994980518,320362547860069042,1709162928241695964
%N A055840 T(2n+6,n), where T is the array in A055830.
%H A055840 G. C. Greubel, <a href="/A055840/b055840.txt">Table of n, a(n) for n = 0..500</a>
%p A055840 with(combinat);
%p A055840 T:= proc(n, k) option remember;
%p A055840 if k<0 or k>n then 0
%p A055840 elif k=0 then fibonacci(n+1)
%p A055840 elif n=1 and k=1 then 0
%p A055840 else T(n-1, k-1) + T(n-1, k) + T(n-2, k)
%p A055840 fi; end:
%p A055840 seq(T(2*n+6, n), n=0..30); # _G. C. Greubel_, Jan 21 2020
%t A055840 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 *)
%o A055840 (Sage)
%o A055840 @CachedFunction
%o A055840 def T(n, k):
%o A055840 if (k<0 and k>n): return 0
%o A055840 elif (k==0): return fibonacci(n+1)
%o A055840 elif (n==1 and k==1): return 0
%o A055840 else: return T(n-1, k-1) + T(n-1, k) + T(n-2, k)
%o A055840 [T(2*n+6, n) for n in (0..30)] # _G. C. Greubel_, Jan 21 2020
%Y A055840 Cf. A055830.
%K A055840 nonn
%O A055840 0,1
%A A055840 _Clark Kimberling_, May 28 2000
%E A055840 Terms a(19) onward added by _G. C. Greubel_, Jan 21 2020