OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, T[2 n, n] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 20 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026519
if (k<0 or k>2*n): return 0
elif (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+1)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(2*n, n) for n in (0..40)] # G. C. Greubel, Dec 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(20) onward added by G. C. Greubel, Dec 20 2021
STATUS
approved