%I #12 Apr 14 2022 01:21:00

%S 1,6,35,204,1199,7089,42070,250269,1491262,8896310,53118352,317373194,

%T 1897253203,11346582851,67882263130,406231442387,2431626954934,

%U 14558306758418,87177151134954,522110098886882,3127380060424476,18734897945679836,112245303177542790,672552484035697364,4030148584900522009

%N a(n) = Sum_{j=0..2*n} Sum_{k=0..j} A026536(j, k).

%H G. C. Greubel, <a href="/A352972/b352972.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Sum_{j=0..2*n} Sum_{k=0..j} A026536(j, k).

%t 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 A352972[n_]:= A352972[n]= Sum[T[j,k], {j,0,2*n}, {k,0,j}];

%t Table[A352972[n], {n,0,40}]

%o (SageMath)

%o @CachedFunction

%o def T(n, k): # A026536

%o if k == 0 or k == 2*n: return 1

%o elif k == 1 or k == 2*n-1: return n//2

%o elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)

%o return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)

%o def A352972(n): return sum(sum(T(j,k) for k in (0..j)) for j in (0..2*n))

%o [A352972(n) for n in (3..40)]

%Y Cf. A026536, A026550.

%K nonn

%O 0,2

%A _G. C. Greubel_, Apr 12 2022