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 A026779 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026769. 11
 1, 1, 2, 3, 6, 10, 17, 32, 56, 97, 181, 322, 567, 1053, 1892, 3369, 6241, 11286, 20255, 37463, 68044, 122809, 226896, 413376, 749159, 1382990, 2525162, 4590351, 8468738, 15487526, 28218889, 52035094, 95273724, 173898941 (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 n=2 and k=1 then 2;    elif 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, Nov 01 2019 MATHEMATICA T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[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, Nov 01 2019 *) PROG (Sage) @CachedFunction def T(n, k):     if (k==0 or k==n): return 1     elif (n==2 and k==1): return 2     elif (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, Nov 01 2019 CROSSREFS Cf. A026769, A026770, A026771, A026772, A026773, A026774, A026775, A026776, A026777, A026778. Sequence in context: A233268 A026397 A193200 * A081028 A325232 A208479 Adjacent sequences:  A026776 A026777 A026778 * A026780 A026781 A026782 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 8 19:21 EST 2021. Contains 349596 sequences. (Running on oeis4.)