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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

Clark Kimberling

STATUS

approved

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