A026527 a(n) = T(2*n, n-2), where T is given by A026519.

1, 3, 14, 55, 231, 952, 3976, 16614, 69750, 293557, 1238952, 5240599, 22212645, 94318875, 401143304, 1708558480, 7286677479, 31113264579, 132994055090, 569048532612, 2437033824302, 10445705817063, 44807461337160, 192342179361800, 826205908069555, 3551172735996756, 15272395383833658

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.

Cf. A026536.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/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 = A026519 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, T[2*n, n-2] ];
Table[a[n], {n,2,40}] (* G. C. Greubel, Dec 20 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+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(2*n,n-2) for n in (2..40)] # G. C. Greubel, Dec 20 2021

Formula

a(n) = A026519(2*n, n-2).

a(n) = A026536(2*n, n-2).

Extensions

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