OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} A026536(n, k).
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[Sum[T[n, k], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, Apr 12 2022 *)
PROG
(SageMath)
@CachedFunction
def T(n, k): # A026536
if 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 A026548(n): return sum(T(n, k) for k in (0..n))
[A026548(n) for n in (0..40)] # G. C. Greubel, Apr 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Missing a(0)=1 inserted by Sean A. Irvine, Oct 06 2019
STATUS
approved