A026768 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758.

1, 1, 2, 3, 6, 9, 16, 29, 46, 82, 145, 237, 421, 737, 1228, 2171, 3788, 6388, 11253, 19617, 33344, 58597, 102141, 174571, 306294, 533976, 916309, 1605975, 2800260, 4820020, 8441365, 14721208, 25399974, 44458045, 77542951

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), 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], {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, 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, A026766, A026767.

Sequence in context: A327475 A017915 A114702 * A068604 A174023 A014868

Adjacent sequences: A026765 A026766 A026767 * A026769 A026770 A026771

Keyword

nonn

Author

Clark Kimberling

Status

approved