A026559 a(n) = T(2*n, n-1), where T is given by A026552.

1, 3, 12, 45, 180, 721, 2940, 12069, 49935, 207691, 867900, 3640429, 15319395, 64643580, 273431408, 1158988141, 4921651521, 20934115963, 89173404140, 380355072153, 1624282578215, 6943928981859, 29715239620368, 127276313406125, 545605497876400, 2340694589348376, 10048952593607088, 43170264470594302

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026560, A026563, A026566, A026567, A027272, A027273, A027274, 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}, T[2*n, n-1]];
Table[a[n], {n,40}] (* G. C. Greubel, Dec 17 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)
[T(2*n,n-1) for n in (1..40)] # G. C. Greubel, Dec 17 2021

Formula

a(n) = A026552(2*n, n-1)

Extensions

Terms a(20) onward added by G. C. Greubel, Dec 17 2021