A027273 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A026552.

2, 16, 52, 428, 1516, 12792, 46936, 402164, 1504432, 13015480, 49288856, 429204354, 1639174304, 14340670000, 55108565584, 483825847108, 1868067054968, 16445659005424, 63734526307552, 562323306397388, 2185849699156352, 19320211642880176, 75288454939134992

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{k=0..2*n-1} A026552(n, k)*A026552(n, k+1).

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+1], {k, 0, 2*n-1}]];
Table[a[n], {n, 0, 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+1) for k in (0..2*n-1) )
[a(n) for n in (1..40)] # G. C. Greubel, Dec 18 2021

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027272, A027274, A027275, A027276.

Sequence in context: A090453 A006885 A220139 * A210710 A337529 A225051

Adjacent sequences: A027270 A027271 A027272 * A027274 A027275 A027276

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved