A026779 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026769.

1, 1, 2, 3, 6, 10, 17, 32, 56, 97, 181, 322, 567, 1053, 1892, 3369, 6241, 11286, 20255, 37463, 68044, 122809, 226896, 413376, 749159, 1382990, 2525162, 4590351, 8468738, 15487526, 28218889, 52035094, 95273724, 173898941

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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), k=0..floor(n/2)), 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], {k, 0, Floor[n/2]}], {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, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Nov 01 2019

Crossrefs

Cf. A026769, A026770, A026771, A026772, A026773, A026774, A026775, A026776, A026777, A026778.

Sequence in context: A233268 A026397 A193200 * A081028 A325232 A208479

Adjacent sequences: A026776 A026777 A026778 * A026780 A026781 A026782

Keyword

nonn

Author

Clark Kimberling

Status

approved