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A026555 a(n) = T(n, n-2), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 2.

%I A026555 #8 Dec 17 2021 20:55:51
%S A026555 1,2,7,13,40,76,226,434,1279,2470,7267,14085,41462,80584,237484,
%T A026555 462620,1365014,2664276,7870226,15387670,45501743,89097932,263707094,
%U A026555 517058502,1531614109,3006637946,8912678569,17514547015,51952990090
%N A026555 a(n) = T(n, n-2), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 2.
%H A026555 G. C. Greubel, <a href="/A026555/b026555.txt">Table of n, a(n) for n = 2..1000</a>
%F A026555 a(n) = A026552(n, n-2).
%t A026555 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
%t A026555 Table[T[n,n-2], {n,2,40}] (* _G. C. Greubel_, Dec 17 2021 *)
%o A026555 (Sage)
%o A026555 @CachedFunction
%o A026555 def T(n,k): # T = A026552
%o A026555     if (k==0 or k==2*n): return 1
%o A026555     elif (k==1 or k==2*n-1): return (n+2)//2
%o A026555     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026555     else: return T(n-1, k) + T(n-1, k-2)
%o A026555 [T(n,n-2) for n in (1..40)] # _G. C. Greubel_, Dec 17 2021
%Y A026555 Cf. A026552, A026553, A026554, A026556, A026557, A026558, A026559, A026560, A026563, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K A026555 nonn
%O A026555 2,2
%A A026555 _Clark Kimberling_