A027284 a(n) = Sum_{k=0..2*n-2} T(n,k) * T(n,k+2), with T given by A026584.

5, 28, 167, 1024, 6359, 39759, 249699, 1573524, 9943905, 62994733, 399936573, 2543992514, 16210331727, 103453402718, 661164765879, 4230874777682, 27105456280491, 173838468040879, 1115987495619427, 7170725839251598, 46113396476943241, 296773029762031990

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027285, 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+2], {k, 0, 2*n-2}];
Table[a[n], {n, 2, 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 A027284(n): return sum(T(n,j)*T(n, j+2) for j in (0..2*n-2))
[A027284(n) for n in (2..40)] # G. C. Greubel, Dec 15 2021

Formula

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

Extensions

More terms from Sean A. Irvine, Oct 26 2019