A026547 a(n) = T(n, floor(n/2)), T given by A026536.

1, 1, 1, 1, 5, 6, 16, 19, 65, 79, 251, 306, 1016, 1247, 4117, 5069, 16913, 20889, 69865, 86479, 290455, 360205, 1212905, 1506462, 5085224, 6324176, 21389824, 26630423, 90226449, 112439094, 381519416, 475838291, 1616684241, 2017827545

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..340

Crossrefs

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/2], If[EvenQ[n], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]];
Table[T[n, Floor[n/2]], {n,0,40}] (* G. C. Greubel, Apr 11 2022 *)

SageMath

@CachedFunction
def T(n, k): # A026536
    if k < 0 or n < 0: return 0
    elif k == 0 or k == 2*n: return 1
    elif k == 1 or k == 2*n-1: return n//2
    elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
    return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
def A026547(n): return T(n, n//2)
[A026547(n) for n in (0..40)] # G. C. Greubel, Apr 11 2022

Formula

a(n) = A026536(n, floor(n/2)).