A027274 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A026552.

10, 40, 342, 1279, 11016, 41462, 359530, 1365014, 11899516, 45501743, 398306769, 1531614109, 13450930624, 51952990090, 457449811458, 1773182087440, 15646091896400, 60825762159338, 537651887201990, 2095280066101886, 18547910336883720, 72432026278468535

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027272, A027273, A027275, A027276.

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)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, k+2], {k, 0, 2*n-2}]];
Table[a[n], {n,2,40}] (* G. C. Greubel, Dec 18 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026552
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+2)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n,k)*T(n,k+2) for k in (0..2*n-2) )
[a(n) for n in (2..40)] # G. C. Greubel, Dec 18 2021

Formula

a(n) = Sum_{k=0..2*n-2} A026552(n,k) * A026552(n,k+2).

Extensions

More terms from Sean A. Irvine, Oct 26 2019