A099779 a(n) = ceiling( 1/2 + (Sum_{i=0..n-1}C(n,i)*C(n,i+1))/2^(n+1) ).

1, 2, 3, 4, 7, 13, 23, 44, 83, 159, 306, 590, 1144, 2220, 4317, 8408, 16399, 32023, 62601, 122498, 239924, 470304, 922612, 1811217, 3558035, 6993883, 13755529, 27068914, 53294747, 104979547, 206880514, 407866454, 804432711, 1587177283

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

Sequence in context: A266498 A137495 A341531 * A270440 A000690 A049876

Adjacent sequences: A099776 A099777 A099778 * A099780 A099781 A099782

Keyword

nonn,easy

Author

Sibasish Ghosh, Simone Severini, Nov 12 2004

Extensions

More terms from Emeric Deutsch, Feb 16 2005

Status

approved