cp's OEIS Frontend

A026550 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.

%I A026550 #10 Apr 13 2022 01:15:40
%S A026550 1,2,6,13,35,77,204,453,1199,2675,7089,15855,42070,94228,250269,
%T A026550 561068,1491262,3345334,8896310,19966310,53118352,119257668,317373194,
%U A026550 712742108,1897253203,4261711183,11346582851,25491926511,67882263130
%N A026550 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.
%H A026550 G. C. Greubel, <a href="/A026550/b026550.txt">Table of n, a(n) for n = 0..1000</a>
%F A026550 a(n) = Sum_{j=0..n} Sum_{k=0..j} A026548(j, k).
%t A026550 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 A026550 A026550[n_]:= A026550[n]= Sum[T[j, k], {j,0,n}, {k,0,j}];
%t A026550 Table[A026550[n], {n,0,40}] (* _G. C. Greubel_, Apr 12 2022 *)
%o A026550 (SageMath)
%o A026550 @CachedFunction
%o A026550 def T(n, k): # A026536
%o A026550     if k == 0 or k == 2*n: return 1
%o A026550     elif k == 1 or k == 2*n-1: return n//2
%o A026550     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026550     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026550 def A026550(n): return sum(sum(T(j,k) for k in (0..j)) for j in (0..n))
%o A026550 [A026550(n) for n in (0..40)] # _G. C. Greubel_, Apr 12 2022
%Y A026550 Cf. A026548.
%K A026550 nonn
%O A026550 0,2
%A A026550 _Clark Kimberling_