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A026541 a(n) = T(n,n-4), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.

%I A026541 #8 Apr 12 2022 01:35:40
%S A026541 1,2,9,19,65,136,430,886,2721,5538,16793,33887,102102,204856,615024,
%T A026541 1229280,3682545,7341786,21963161,43712603,130648089,259726104,
%U A026541 775797750,1541084142,4601346295,9135694750,27270124455,54125522793
%N A026541 a(n) = T(n,n-4), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.
%H A026541 G. C. Greubel, <a href="/A026541/b026541.txt">Table of n, a(n) for n = 4..999</a>
%F A026541 a(n) = A026536(n, n-4).
%t A026541 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]] ]];
%t A026541 Table[T[n, n-4], {n, 4, 45}] (* _G. C. Greubel_, Apr 11 2022 *)
%o A026541 (SageMath)
%o A026541 @CachedFunction
%o A026541 def T(n, k): # A026536
%o A026541     if k < 0 or n < 0: return 0
%o A026541     elif k == 0 or k == 2*n: return 1
%o A026541     elif k == 1 or k == 2*n-1: return n//2
%o A026541     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026541     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026541 def A026541(n): return T(n,n-4)
%o A026541 [A026541(n) for n in (4..45)] # _G. C. Greubel_, Apr 11 2022
%Y A026541 Cf. A026536.
%K A026541 nonn
%O A026541 4,2
%A A026541 _Clark Kimberling_