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A026540 a(n) = T(n,n-3), T given by A026536. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.

%I A026540 #8 Apr 11 2022 14:57:39
%S A026540 1,2,6,16,36,104,215,635,1275,3786,7518,22344,44170,131264,259002,
%T A026540 769578,1517418,4508580,8888495,26412001,52077234,154773696,305257251,
%U A026540 907432695,1790353357,5323519838,10507386918,31251588060
%N A026540 a(n) = T(n,n-3), T given by A026536. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.
%H A026540 G. C. Greubel, <a href="/A026540/b026540.txt">Table of n, a(n) for n = 3..1000</a>
%F A026540 a(n) = A026536(n, n-3).
%t A026540 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-3], {n,3,40}] (* _G. C. Greubel_, Apr 10 2022 *)
%o A026540 (SageMath)
%o A026540 @CachedFunction
%o A026540 def T(n, k): # A026536
%o A026540     if k < 0 or n < 0: return 0
%o A026540     elif k == 0 or k == 2*n: return 1
%o A026540     elif k == 1 or k == 2*n-1: return n//2
%o A026540     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026540     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026540 def A026540(n): return T(n,n-3)
%o A026540 [A026540(n) for n in (3..40)] # _G. C. Greubel_, Apr 10 2022
%Y A026540 Cf. A026536.
%K A026540 nonn
%O A026540 3,2
%A A026540 _Clark Kimberling_