A026776 a(n) = Sum_{k=0..n} T(n,k), T given by A026769.

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

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=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

Crossrefs

Cf. A026769, A026770, A026771, A026772, A026773, A026774, A026775, A026777, A026778, A026779.

Sequence in context: A319379 A347011 A206301 * A117160 A339156 A247623

Adjacent sequences: A026773 A026774 A026775 * A026777 A026778 A026779

Keyword

nonn

Author

Clark Kimberling

Status

approved