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 A026768 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758. 10
 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 (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 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 STATUS approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)