OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
MAPLE
A026747 := proc(n, k) option remember;
if k=0 or k = n then 1;
elif type(n, 'even') and k <= n/2 then
procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;
else
procname(n-1, k-1)+procname(n-1, k) ;
end if ;
end proc:
seq(add(A026747(n, k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[Sum[T[n, k], Floor[n/2]], {n, 0, 30}] (* G. C. Greubel, Oct 29 2019 *)
PROG
(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
elif (mod(n, 2)==0 and k<=n/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 29 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved