A026732 a(n) = Sum_{k=0..n} T(n,k), T given by A026725.

1, 2, 4, 9, 18, 40, 80, 176, 352, 769, 1538, 3343, 6686, 14477, 28954, 62505, 125010, 269216, 538432, 1157244, 2314488, 4966260, 9932520, 21282622, 42565244, 91096110, 182192220, 389515284, 779030568, 1664015246, 3328030492

Offset

0,2

Links

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

Formula

Conjecture: +(-n+1)*a(n) +2*a(n-1) +3*(3*n-7)*a(n-2) -10*a(n-3) +(-23*n+95)*a(n-4) +6*a(n-5) +(11*n-95)*a(n-6) +2*a(n-7) +4*(n-7)*a(n-8)=0. - R. J. Mathar, Oct 26 2019

Maple

A026732 := proc(n)
    add(A026725(n, k), k=0..n) ;
end proc:
seq(A026732(n), n=0..10) ; # R. J. Mathar, Oct 26 2019

Mathematica

T[n_, k_]:= T[n, k]= 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, n}], {n, 0, 30}] (* G. C. Greubel, Oct 26 2019 *)

Prog

(PARI) T(n, k) = if(k==n || k==0, 1, if(2*k==n-1, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
vector(31, n, sum(k=0, n-1, T(n-1, k)) ) \\ G. C. Greubel, Oct 26 2019
(Sage)
@CachedFunction
def T(n, k):
    if (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..n)) for n in (0..30)] # G. C. Greubel, Oct 26 2019
(GAP)
T:= function(n, k)
    if k=0 or k=n then return 1;
    elif 2*k=n-1 then 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);
    fi;
  end;
List([0..30], n-> Sum([0..n], k-> T(n, k) )); # G. C. Greubel, Oct 26 2019

Crossrefs

Sequence in context: A193201 A038044 A189911 * A171003 A094291 A026765

Adjacent sequences: A026729 A026730 A026731 * A026733 A026734 A026735

Keyword

nonn

Author

Clark Kimberling

Status

approved