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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A085960 Size of the largest code of length 4 and minimum distance 3 over an alphabet of size n. This is usually denoted by A_{n}(4,3).

Original entry on oeis.org

1, 2, 9, 16, 25, 34, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500
Offset: 1

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Author

W. Edwin Clark, Aug 17 2003

Keywords

Comments

For n not 2 and not 6, a code C of size n^2 is given by two orthogonal Latin squares A and B of order n by C = {(i,j,A(i,j),B(i,j)): i,j in {1..n}}. Two orthogonal Latin squares of order n exist if and only if n is not 2 and not 6. See A055495.

Examples

			a(2) = 2 since the code C={0000,1110} has minimum distance 3 over the alphabet {0,1} and there is no such code with more codewords.
		

References

  • Raymond Hill, "A First Course in Coding Theory", Clarendon Press, Oxford, 1986 (see chapter 10, Theorem 10.16)

Crossrefs

Cf. A055495.

Programs

  • Mathematica
    Table[n^2 - 2 (Boole[n == 2] + Boole[n == 6]), {n, 50}] (* Wesley Ivan Hurt, Nov 04 2015 *)
    LinearRecurrence[{3,-3,1},{1,2,9,16,25,34,49,64,81},50] (* Harvey P. Dale, Apr 18 2019 *)
  • PARI
    Vec(-x*(2*x^8-6*x^7+6*x^6-2*x^5+2*x^4-6*x^3+6*x^2-x+1)/(x-1)^3 + O(x^100)) \\ Colin Barker, Nov 04 2015

Formula

a(n) = 2 if n = 2, a(n) = 34 if n = 6, otherwise a(n) = n^2.
From Colin Barker, Nov 04 2015: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>9.
G.f.: -x*(2*x^8-6*x^7+6*x^6-2*x^5+2*x^4-6*x^3+6*x^2-x+1) / (x-1)^3.
(End)

Extensions

More terms from David Wasserman, Feb 16 2005