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A026557 a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.

%I A026557 #10 Dec 18 2021 01:00:03
%S A026557 1,3,12,28,93,201,631,1316,4037,8259,25052,50680,152782,306958,921982,
%T A026557 1844304,5526849,11024331,32987492,65675764,196323853,390374193,
%U A026557 1166171943,2316881892,6918228187,13737041045,41007165500
%N A026557 a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.
%H A026557 G. C. Greubel, <a href="/A026557/b026557.txt">Table of n, a(n) for n = 4..1000</a>
%F A026557 a(n) = A026552(n, n-4).
%t A026557 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 A026557 Table[T[n,n-4], {n,4,40}] (* _G. C. Greubel_, Dec 17 2021 *)
%o A026557 (Sage)
%o A026557 @CachedFunction
%o A026557 def T(n,k): # T = A026552
%o A026557     if (k==0 or k==2*n): return 1
%o A026557     elif (k==1 or k==2*n-1): return (n+2)//2
%o A026557     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026557     else: return T(n-1, k) + T(n-1, k-2)
%o A026557 [T(n,n-4) for n in (4..40)] # _G. C. Greubel_, Dec 17 2021
%Y A026557 Cf. A026552, A026553, A026554, A026555, A026556, A026558, A026559, A026560, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K A026557 nonn
%O A026557 4,2
%A A026557 _Clark Kimberling_