A026538 a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.

1, 1, 3, 6, 13, 33, 65, 180, 346, 990, 1897, 5502, 10571, 30863, 59523, 174456, 337672, 992304, 1926650, 5673140, 11043858, 32571858, 63548069, 187675644, 366849016, 1084649644, 2123604927, 6284986554, 12322549765, 36501029265

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

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, n-1], {n, 35}] (* G. C. Greubel, Apr 10 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 A026538(n): return T(n,n-1)
[A026538(n) for n in (1..35)] # G. C. Greubel, Apr 10 2022

Formula

a(n) = A026536(n, n-1).