A026754 a(n) = Sum{k=0..n} T(n,k), T given by A026747.

1, 2, 5, 10, 24, 48, 114, 228, 540, 1080, 2558, 5116, 12133, 24266, 57658, 115316, 274600, 549200, 1310817, 2621634, 6271788, 12543576, 30076629, 60153258, 144550655, 289101310, 696176322, 1392352644, 3359516328

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Maple

A026747 := proc(n, k) option remember;
   if k=0 or k = n then 1;
   elif type(n, 'even') and k <= n/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(A026747(n, k), k=0..n), n=0..30); # G. C. Greubel, Oct 29 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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, n}], {n, 0, 30}] (* G. C. Greubel, Oct 29 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==0 and k<=n/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..n)) for n in (0..30)] # G. C. Greubel, Oct 29 2019

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026755, A026756, A026757.

Sequence in context: A361505 A299436 A049937 * A291247 A316697 A032170

Adjacent sequences: A026751 A026752 A026753 * A026755 A026756 A026757

Keyword

nonn

Author

Clark Kimberling

Status

approved