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

0,2

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(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 *)

Prog

(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

Crossrefs

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

Sequence in context: A240745 A227682 A099325 * A023523 A065979 A106463

Adjacent sequences: A026775 A026776 A026777 * A026779 A026780 A026781

Keyword

nonn

Author

Clark Kimberling

Status

approved