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
KEYWORD
nonn
AUTHOR
STATUS
approved