A026777 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026769.

1, 1, 3, 5, 14, 26, 70, 138, 362, 742, 1912, 4028, 10249, 22033, 55547, 121273, 303641, 670997, 1671233, 3729071, 9250099, 20803231, 51437219, 116436313, 287152067, 653567143, 1608416195, 3677760541, 9035150126, 20741496354

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=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, 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) 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, A026778, A026779.

Sequence in context: A104208 A378262 A364314 * A007136 A145974 A147544

Adjacent sequences: A026774 A026775 A026776 * A026778 A026779 A026780

Keyword

nonn

Author

Clark Kimberling

Status

approved