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A026556 a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.

%I A026556 #7 Dec 17 2021 20:55:58
%S A026556 1,3,8,24,52,156,319,954,1910,5696,11304,33648,66514,197778,390266,
%T A026556 1159844,2286996,6795576,13397075,39809076,78489235,233262931,
%U A026556 460030947,1367463642,2697786052,8021305890,15830906756,47082494816
%N A026556 a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.
%H A026556 G. C. Greubel, <a href="/A026556/b026556.txt">Table of n, a(n) for n = 3..1000</a>
%F A026556 a(n) = A026552(n, n-3).
%t A026556 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 A026556 Table[T[n,n-3], {n,3,40}] (* _G. C. Greubel_, Dec 17 2021 *)
%o A026556 (Sage)
%o A026556 @CachedFunction
%o A026556 def T(n,k): # T = A026552
%o A026556     if (k==0 or k==2*n): return 1
%o A026556     elif (k==1 or k==2*n-1): return (n+2)//2
%o A026556     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026556     else: return T(n-1, k) + T(n-1, k-2)
%o A026556 [T(n,n-3) for n in (3..40)] # _G. C. Greubel_, Dec 17 2021
%Y A026556 Cf. A026552, A026553, A026554, A026555, A026557, A026558, A026559, A026560, A026563, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.
%K A026556 nonn
%O A026556 3,2
%A A026556 _Clark Kimberling_