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A026776
a(n) = Sum_{k=0..n} T(n,k), T given by A026769.
11
1, 2, 4, 9, 19, 43, 93, 212, 466, 1070, 2382, 5506, 12386, 28800, 65356, 152745, 349183, 819639, 1885361, 4441719, 10270279, 24269629, 56363319, 133529869, 311255601, 738947515, 1727873793, 4109314729, 9634406661, 22946573863
OFFSET
0,2
LINKS
MAPLE
T:= proc(n, k) option remember;
if n<0 then 0;
elif k=0 or k=n then 1;
elif n=2 and k=1 then 2;
elif k <= (n-1)/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(T(n, k), k=0..n), n=0..30); # G. C. Greubel, Nov 01 2019
MATHEMATICA
T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[k<=(n-1)/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], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Nov 01 2019 *)
PROG
(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
elif (n==2 and k==1): return 2
elif (k<=(n-1)/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..n)) for n in (0..30)] # G. C. Greubel, Nov 01 2019
KEYWORD
nonn
STATUS
approved