A026525 a(n) = T(2*n, n), where T is given by A026519.

1, 1, 5, 16, 65, 251, 1016, 4117, 16913, 69865, 290455, 1212905, 5085224, 21389824, 90226449, 381519416, 1616684241, 6863544233, 29187402749, 124305180842, 530108333515, 2263423401745, 9674857844129, 41396075156859, 177285394355336, 759895396193376, 3259667597627576, 13992851410449865

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026526, A026527, 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, 0, 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] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 20 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026519
    if (k<0 or k>2*n): return 0
    elif (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) for n in (0..40)] # G. C. Greubel, Dec 20 2021

Formula

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

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

Extensions

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