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.
%I A085960 #12 Apr 18 2019 10:59:30 %S A085960 1,2,9,16,25,34,49,64,81,100,121,144,169,196,225,256,289,324,361,400, %T A085960 441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,1225,1296, %U A085960 1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401,2500 %N 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). %C A085960 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. %D A085960 Raymond Hill, "A First Course in Coding Theory", Clarendon Press, Oxford, 1986 (see chapter 10, Theorem 10.16) %H A085960 Colin Barker, <a href="/A085960/b085960.txt">Table of n, a(n) for n = 1..1000</a> %H A085960 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A085960 a(n) = 2 if n = 2, a(n) = 34 if n = 6, otherwise a(n) = n^2. %F A085960 From _Colin Barker_, Nov 04 2015: (Start) %F A085960 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>9. %F A085960 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. %F A085960 (End) %e A085960 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. %t A085960 Table[n^2 - 2 (Boole[n == 2] + Boole[n == 6]), {n, 50}] (* _Wesley Ivan Hurt_, Nov 04 2015 *) %t A085960 LinearRecurrence[{3,-3,1},{1,2,9,16,25,34,49,64,81},50] (* _Harvey P. Dale_, Apr 18 2019 *) %o A085960 (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 %Y A085960 Cf. A055495. %K A085960 easy,nonn %O A085960 1,2 %A A085960 _W. Edwin Clark_, Aug 17 2003 %E A085960 More terms from _David Wasserman_, Feb 16 2005