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 A026766 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758. 10
 1, 1, 3, 5, 13, 24, 59, 115, 273, 552, 1278, 2655, 6031, 12795, 28632, 61775, 136572, 298764, 653948, 1447225, 3141427, 7020833, 15132512, 34106865, 73069892, 165903082, 353576829, 807957495, 1714132308, 3939206346 (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=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, 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) 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, A026767, A026768. Sequence in context: A005824 A336103 A027305 * A026709 A219699 A320330 Adjacent sequences:  A026763 A026764 A026765 * A026767 A026768 A026769 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 30 11:07 EST 2021. Contains 349419 sequences. (Running on oeis4.)