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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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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 *) -
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