A026537 a(n) = T(n,n), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n)=0.

1, 0, 2, 2, 8, 12, 38, 66, 196, 360, 1052, 1980, 5774, 11004, 32146, 61726, 180772, 348912, 1024256, 1984608, 5837908, 11346280, 33433996, 65143716, 192239854, 375351288, 1109049320, 2169299288, 6416509142, 12569973108

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026521, 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, n], {n, 0, 35}] (* G. C. Greubel, Apr 10 2022 *)

SageMath

@cached_function
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 A026537(n): return T(n,n)
[A026537(n) for n in (0..35)] # G. C. Greubel, Apr 10 2022

Formula

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

a(n) = 2 * A026521(n-1).