cp's OEIS Frontend

A026538 a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.

%I A026538 #8 Apr 11 2022 08:59:06
%S A026538 1,1,3,6,13,33,65,180,346,990,1897,5502,10571,30863,59523,174456,
%T A026538 337672,992304,1926650,5673140,11043858,32571858,63548069,187675644,
%U A026538 366849016,1084649644,2123604927,6284986554,12322549765,36501029265
%N A026538 a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.
%H A026538 G. C. Greubel, <a href="/A026538/b026538.txt">Table of n, a(n) for n = 1..1000</a>
%F A026538 a(n) = A026536(n, n-1).
%t A026538 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-1], {n, 35}] (* _G. C. Greubel_, Apr 10 2022 *)
%o A026538 (SageMath)
%o A026538 @CachedFunction
%o A026538 def T(n, k): # A026536
%o A026538     if k < 0 or n < 0: return 0
%o A026538     elif k == 0 or k == 2*n: return 1
%o A026538     elif k == 1 or k == 2*n-1: return n//2
%o A026538     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026538     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026538 def A026538(n): return T(n,n-1)
%o A026538 [A026538(n) for n in (1..35)] # _G. C. Greubel_, Apr 10 2022
%Y A026538 Cf. A026536.
%K A026538 nonn
%O A026538 1,3
%A A026538 _Clark Kimberling_