OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
Radoslav Derka, Vladimir Buzek, Artur Ekert, Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles, Phys. Rev. Lett. 80 (1998) 1571-1575.
FORMULA
a(n) = ceiling(1/2 + n*binomial(2*n,n) / ((n+1) * 2^(n+1))). - Vaclav Kotesovec, Sep 04 2019
MAPLE
a:=n->ceil((1/2)+(1/(2^(n+1))*sum(binomial(n, i)*binomial(n, i+1), i=0..n-1))): seq(a(n), n=2..36); # Emeric Deutsch, Feb 16 2005
MATHEMATICA
Table[Ceiling[1/2 + Sum[Binomial[n, j]*Binomial[n, j+1], {j, 0, n-1}]/2^(n+1) ], {n, 2, 40}] (* G. C. Greubel, Sep 04 2019 *)
Table[Ceiling[1/2 + n*Binomial[2*n, n] / ((n + 1)*2^(n + 1))], {n, 2, 40}] (* Vaclav Kotesovec, Sep 04 2019 *)
PROG
(PARI) a(n) = ceil(1/2 + sum(j=0, n-1, binomial(n, j)*binomial(n, j+1) )/2^(n+1)); \\ G. C. Greubel, Sep 04 2019
(Magma) [Ceiling(1/2 + &+[Binomial(n, j)*Binomial(n, j+1): j in [0..n-1] ]/2^(n+1) ): n in [2..40]]; // G. C. Greubel, Sep 04 2019
(Sage) [ceil(1/2 + sum(binomial(n, j)*binomial(n, j+1) for j in (0..n-1) )/2^(n+1)) for n in (2..40)] # G. C. Greubel, Sep 04 2019
(GAP) Concatenation([1], List([3..40], n-> Int(3/2 + Sum([0..n], j-> (n-j)*Binomial(n, j)^2/(j+1))/2^(n+1) ))); # G. C. Greubel, Sep 04 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sibasish Ghosh, Simone Severini, Nov 12 2004
EXTENSIONS
More terms from Emeric Deutsch, Feb 16 2005
STATUS
approved