0,4

Guenther Rosenbaum showed that the sequence represents the optimal number of guesses in the static Mastermind game with two pegs. Namely, the optimal number of static guesses equals 2k, if the number of colors is either (3k - 1) or 3k and is (2k + 1), if the number of colors is (3k + 1), k >= 1. - Alex Bogomolny, Mar 06, 2002

First differences are in A011655. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008

Index entries for sequences related to linear recurrences with constant coefficients

G. Rosenbaum, More information

See also Static Mastermind Game

G.f.: (x^2+2*x^3+2*x^4+x^5)/(1-x^3)^2 - Len Smiley (smiley(AT)math.uaa.alaska.edu)

a(n)=Floor(2n/3)

a(0)=a(1)=0 a(n)=n-1-floor(u(n-1)/2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 26 2002

a(n)=a(n-1)+(1/2)((-1)^Floor[(2n+2)/3]+1), a(0)=0. - Mario Catalani (mario.catalani(AT)unito.it), Oct 20 2003

a(n)=sum{k=0..n-1, mod(Fib(k), 2)}; - Paul Barry (pbarry(AT)wit.ie), May 31 2005

a(n) = A004773(n) - A004396(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2005

O.g.f.: x^2*(1+x)/[(-1+x)^2*(1+x+x^2)] . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008

a(n)=2*(-1+Sum{k=0..n}{1/9*[ -2*(k mod 3)+((k+1) mod 3)+4*((k+2) mod 3)]}+{[(n+2) mod 3] mod 2}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 02 2008]

Table[ Floor[2n/3], {n, 0, 75} ]

Cf. A004396.

Zero followed by partial sums of A011655.

Sequence in context: A020915 A156301 A032509 this_sequence A038372 A121930 A020909

Adjacent sequences: A004520 A004521 A004522 this_sequence A004524 A004525 A004526

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 06 2002