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 A026790 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026780. 11
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 19 01:02 EDT 2024. Contains 376002 sequences. (Running on oeis4.)