A026766 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758.

1, 1, 3, 5, 13, 24, 59, 115, 273, 552, 1278, 2655, 6031, 12795, 28632, 61775, 136572, 298764, 653948, 1447225, 3141427, 7020833, 15132512, 34106865, 73069892, 165903082, 353576829, 807957495, 1714132308, 3939206346

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 type(n, 'odd') and 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, Oct 31 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && 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, Oct 31 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (mod(n, 2)==1 and 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, Oct 31 2019

Crossrefs

Cf. A026758, A026759, A026760, A026761, A026762, A026763, A026764, A026765, A026767, A026768.

Sequence in context: A005824 A336103 A027305 * A026709 A219699 A320330

Adjacent sequences: A026763 A026764 A026765 * A026767 A026768 A026769

Keyword

nonn

Author

Clark Kimberling

Status

approved