A026755 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.

1, 1, 4, 5, 18, 25, 84, 124, 398, 612, 1901, 3012, 9126, 14800, 43968, 72658, 212417, 356544, 1028520, 1749344, 4989477, 8583258, 24244139, 42121079, 117973702, 206754379, 574811040, 1015179978, 2803969443, 4986329826

Offset

0,3

Links

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

Maple

A026747 := proc(n, k) option remember;
   if k=0 or k = n then 1;
   elif type(n, 'even') and k <= n/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(A026747(n, k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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], Floor[n/2]], {n, 0, 30}] (* G. C. Greubel, Oct 29 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==0 and k<=n/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, Oct 29 2019

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026756, A026757.

Sequence in context: A243297 A357366 A026902 * A368029 A243120 A317378

Adjacent sequences: A026752 A026753 A026754 * A026756 A026757 A026758

Keyword

nonn

Author

Clark Kimberling

Status

approved