A026563 a(n) = T(n, floor(n/2)), where T is given by A026552.

1, 1, 2, 2, 7, 8, 24, 28, 93, 111, 362, 436, 1452, 1763, 5880, 7176, 24089, 29521, 99386, 122182, 412637, 508595, 1721500, 2126312, 7211536, 8923136, 30312960, 37563930, 127790379, 158563368, 540082784, 670893296, 2287577537

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, 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[n, Floor[n/2]]];
Table[a[n], {n,0,40}] (* 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)
[T(n,n//2) for n in (0..40)] # G. C. Greubel, Dec 18 2021

Formula

a(n) = A026552(n, floor(n/2)).