%I #12 Dec 15 2021 07:13:37

%S 12,116,682,4908,30272,201648,1273286,8275894,52783298,340392020,

%T 2180905198,14035736838,90149817980,580197442656,3732734480794,

%U 24041345351898,154874693823022,998441294531516,6439238635990250,41552345665859196,268252644944872486

%N a(n) = Sum_{k=0..2*n-3} T(n,k) * T(n,k+3), with T given by A026584.

%H G. C. Greubel, <a href="/A027285/b027285.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = Sum_{k=0..2*n-3} A026584(n,k) * A026584(n,k+3).

%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+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)

%t a[n_]:= a[n]= Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}];

%t Table[a[n], {n, 3, 40}] (* _G. C. Greubel_, Dec 15 2021 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k): # T = A026584

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

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

%o else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)

%o @CachedFunction

%o def A027285(n): return sum(T(n,j)*T(n, j+3) for j in (0..2*n-3))

%o [A027285(n) for n in (3..40)] # _G. C. Greubel_, Dec 15 2021

%Y Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027286.

%K nonn

%O 3,1

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Oct 26 2019