A027285 a(n) = Sum_{k=0..2*n-3} T(n,k) * T(n,k+3), with T given by A026584.

12, 116, 682, 4908, 30272, 201648, 1273286, 8275894, 52783298, 340392020, 2180905198, 14035736838, 90149817980, 580197442656, 3732734480794, 24041345351898, 154874693823022, 998441294531516, 6439238635990250, 41552345665859196, 268252644944872486

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

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

Programs

Mathematica

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 *)
a[n_]:= a[n]= Sum[T[n, k]*T[n, k+3], {k, 0, 2*n-3}];
Table[a[n], {n, 3, 40}] (* G. C. Greubel, Dec 15 2021 *)

Sage

@CachedFunction
def T(n, k):  # T = A026584
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n//2)
    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)
@CachedFunction
def A027285(n): return sum(T(n,j)*T(n, j+3) for j in (0..2*n-3))
[A027285(n) for n in (3..40)] # G. C. Greubel, Dec 15 2021

Formula

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

Extensions

More terms from Sean A. Irvine, Oct 26 2019