A026547 - OEIS

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

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OFFSET

0,5

LINKS

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

FORMULA

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

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 *)

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 A026547(n): return T(n, n//2)

[A026547(n) for n in (0..40)] # G. C. Greubel, Apr 11 2022