A026545 a(n) = T(2n-1, n-1), T given by A026536.

1, 1, 6, 19, 79, 306, 1247, 5069, 20889, 86479, 360205, 1506462, 6324176, 26630423, 112439094, 475838291, 2017827545, 8572102713, 36474080228, 155418445421, 663102388605, 2832471934357, 12111891668431, 51841780973922, 222092855692496, 952237575555176, 4085873505697131, 17544024146446621

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..300

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[2*n-1, n-1], {n,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 A026545(n): return T(2*n-1, n-1)
[A026545(n) for n in (1..40)] # G. C. Greubel, Apr 11 2022

Formula

a(n) = A026536(2*n-1, n-1).

Extensions

Terms a(20) onward added by G. C. Greubel, Apr 11 2022