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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

Clark Kimberling

STATUS

approved

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