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

2,1

Links

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A118266 A054885 A000449 * A253674 A016082 A346346

Adjacent sequences: A027271 A027272 A027273 * A027275 A027276 A027277

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved