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A060542
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(1/6)*multinomial(3n;n,n,n).
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3
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1, 15, 280, 5775, 126126, 2858856, 66512160, 1577585295, 37978905250, 925166131890, 22754499243840, 564121960420200, 14079683012144400, 353428777651788000, 8915829964229105280, 225890910734335847055
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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)
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
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FORMULA
| a(n) = (3n!)/(n!^3*6) = a(n-1)*3*(3n-1)*(3n-2)/n^2 = A060540(3, n) = A006480(n)/6.
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PROG
| (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]
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CROSSREFS
| Cf. A025035.
Sequence in context: A034687 A159239 A199096 * A095654 A177074 A069405
Adjacent sequences: A060539 A060540 A060541 * A060543 A060544 A060545
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001
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EXTENSIONS
| Definition revised by N. J. A. Sloane (njas(AT)research.att.com), Feb 02 2009
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