A026545 - OEIS

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

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OFFSET

1,3

LINKS

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

FORMULA

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

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 *)

PROG

(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