OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = A026584(n, n).
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+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:= a[n]= Block[{$RecursionLimit= Infinity}, T[2*n, n]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 13 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026584
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
[T(2*n, n) for n in (0..40)] # G. C. Greubel, Dec 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(19) onward from G. C. Greubel, Dec 13 2021
STATUS
approved