A026778 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026769.

1, 3, 7, 16, 35, 78, 171, 383, 849, 1919, 4301, 9807, 22193, 50993, 116349, 269094, 618277, 1437916, 3323277, 7764996, 18035275, 42304904, 98668223, 232198092, 543453693, 1282401208, 3010275001, 7119589730, 16753996391

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026769, A026770, A026771, A026772, A026773, A026774, A026775, A026776, A026777, A026779.

Programs

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(add(T(j,k), k=0..n), j=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[j,k], {k,0,n}, {j,0,n}], {n,0,30}] (* G. C. Greubel, Nov 01 2019 *)

Sage

@CachedFunction
def T(n, k):
    if n < 0:
        return 0
    elif (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(sum(T(j,k) for k in (0..n)) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 01 2019