1,2

Number of ways of dividing 3n labeled items into 3 unlabeled boxes with n items in each box.

Contribution from Antonio Campello (campello(AT)ime.unicamp.br), Nov 11 2009: (Start)

A060542(t) is the number of optimal [n,2,d] binary codes that correct at most t errors, i.e,

having Hamming distance 2t+1 (achieved on length n = 3t+2). These codes are all isometric.

It is also the number of optimal [n,2,d] binary codes that detect 2t+1 errors, i.e.,

having Hamming distance 2t+2 (obtained by adding an overall parity check to the n = 3t+2 optimal codes). These codes are also all isometric.

For t = 0, we have the famous MDS, cyclic, simplex code {(000), (101), (110), (011)}. (End)

Harry J. Smith, Table of n, a(n) for n=1,...,100

a(n) = (3n!)/(n!^3*6) = a(n-1)*3*(3n-1)*(3n-2)/n^2 = A060540(3, n) = A006480(n)/6.

(PARI) { a=1/6; for (n=1, 100, write("b060542.txt", n, " ", a=a*3*(3*n - 1)*(3*n - 2)/n^2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]

Cf. A025035.

Sequence in context: A156091 A034687 A159239 this_sequence A095654 A069405 A125055

Adjacent sequences: A060539 A060540 A060541 this_sequence A060543 A060544 A060545

nonn,new

Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001

Definition revised by N. J. A. Sloane (njas(AT)research.att.com), Feb 02 2009