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

2,1

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027285, A027286.

Sequence in context: A025174 A371778 A083316 * A069731 A272046 A370025

Adjacent sequences: A027281 A027282 A027283 * A027285 A027286 A027287

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved