A026790 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026780.

1, 1, 2, 4, 7, 12, 23, 41, 72, 135, 243, 432, 804, 1455, 2608, 4836, 8785, 15838, 29306, 53385, 96654, 178600, 326019, 592140, 1093135, 1998537, 3638700, 6712659, 12287071, 22412784, 41325279, 75712253, 138308808, 254912873

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 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) ;
    fi ;
end proc:
seq( add(T(n-k, k), k=0..floor(n/2)), n=0..40); # G. C. Greubel, Nov 02 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[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, k], {k, 0, Floor[n/2]}], {n, 0, 40}] (* G. C. Greubel, Nov 02 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (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, k) for k in (0..floor(n/2))) for n in (0..40)] # G. C. Greubel, Nov 02 2019

Crossrefs

Cf. A026780, A026781, A026782, A026783, A026784, A026785, A026786, A026787, A026788, A026789.

Sequence in context: A299023 A007323 A099604 * A054165 A054171 A018080

Adjacent sequences: A026787 A026788 A026789 * A026791 A026792 A026793

Keyword

nonn

Author

Clark Kimberling

Status

approved