A027987 a(n) = Sum_{k=0..2*n-3} T(n, k)*T(n, k+3), T given by A027960.

58, 272, 1154, 4757, 19378, 78422, 315994, 1269270, 5086294, 20345092, 81265106, 324240331, 1292556986, 5149091916, 20500830986, 81586994576, 324577199086, 1290904257426, 5133037194706, 20407032157936, 81119882902118

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A027960.

Programs

Magma

f:= func< n,k | (&+[Binomial(2*n-k+j,j)*Lucas(2*(k-n-j)): j in [0..k-n-1]]) >;
A027960:= func< n,k | k le n select Lucas(k+1) else Lucas(k+1) - f(n,k) >;
A027987:= func< n | (&+[A027960(n,k)*A027960(n,k+3): k in [0..2*n-3]]) >;
[A027987(n): n in [3..40]]; // G. C. Greubel, Jun 14 2025

Mathematica

T[n_, k_]:= T[n,k]= If[k2*n, 0, T[n-1,k-1] + T[n-1,k-2]]];
A027987[n_]:= A027987[n]= Sum[T[n,k]*T[n,k+3], {k,0,2*n-3}]; (* T = A027960 *)
Table[A027987[n], {n,3,50}] (* G. C. Greubel, Jun 14 2025 *)

SageMath

@CachedFunction
def T(n, k): # T = A027960
    if (k>2*n): return 0
    elif (kA027987(n): return sum(T(n,k)*T(n,k+3) for k in range(2*n-2))
print([A027987(n) for n in range(2,41)]) # G. C. Greubel, Jun 14 2025

Formula

a(n) = A000032(n)^2 - 9 + Sum_{k=n-2..2*n-3} A027960(n,k)*A027960(n,k+3). - G. C. Greubel, Jun 14 2025