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A026539 a(n) = T(n,n-2), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.

%I A026539 #8 Apr 11 2022 14:57:24
%S A026539 1,1,5,8,27,49,150,284,845,1625,4797,9288,27377,53207,156900,305720,
%T A026539 902394,1761882,5205950,10181720,30114073,58983859,174609162,
%U A026539 342449340,1014555607,1992082339,5906040623,11608506392,34438443075
%N A026539 a(n) = T(n,n-2), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.
%H A026539 G. C. Greubel, <a href="/A026539/b026539.txt">Table of n, a(n) for n = 2..1000</a>
%F A026539 a(n) = A026536(n, n-2).
%t A026539 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k], T[n-1, k-2] + T[n-1, k]] ]]; Table[T[n,n-2], {n,2,35}] (* _G. C. Greubel_, Apr 10 2022 *)
%o A026539 (SageMath)
%o A026539 @CachedFunction
%o A026539 def T(n, k): # A026536
%o A026539     if k < 0 or n < 0: return 0
%o A026539     elif k == 0 or k == 2*n: return 1
%o A026539     elif k == 1 or k == 2*n-1: return n//2
%o A026539     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026539     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026539 def A026539(n): return T(n,n-2)
%o A026539 [A026539(n) for n in (2..35)] # _G. C. Greubel_, Apr 10 2022
%Y A026539 Cf. A026536.
%K A026539 nonn
%O A026539 2,3
%A A026539 _Clark Kimberling_