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A026777 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026769. 11
1, 1, 3, 5, 14, 26, 70, 138, 362, 742, 1912, 4028, 10249, 22033, 55547, 121273, 303641, 670997, 1671233, 3729071, 9250099, 20803231, 51437219, 116436313, 287152067, 653567143, 1608416195, 3677760541, 9035150126, 20741496354 (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=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, 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) 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, A026778, A026779.

Sequence in context: A026667 A295359 A104208 * A007136 A145974 A147544

Adjacent sequences:  A026774 A026775 A026776 * A026778 A026779 A026780

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 15 08:35 EST 2019. Contains 329144 sequences. (Running on oeis4.)