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%I #22 Sep 08 2022 08:45:13
%S 0,0,0,0,0,0,1,1,2,3,3,4,5,6,7,8,9,11,12,14,15,17,18,21,22,25,26,29,
%T 30,33,35,38,40,44,45,49,51,55,57,61,63,68,70,75,77,82,84,90,92,98,
%U 100,106,108,114,117,123,126,133,135,142,145,152,155,162,165
%N Johnson bound J(n,4,2).
%C A quasipolynomial of order 24 and degree 2. - _Charles R Greathouse IV_, Aug 25 2017
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 527, Cor. 5.
%H Charles R Greathouse IV, <a href="/A091848/b091848.txt">Table of n, a(n) for n = 1..10000</a>
%H W. Chu and C. J. Colbourn, <a href="https://doi.org/10.1016/S0012-365X(03)00266-8">Optimal (n,4,2)-OCC of small orders</a>, Discrete Math., 279 (2004), 163-172.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Johnson_bound">Johnson bound</a>
%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1, -1,1).
%F a(n) = n^2/24 - O(n). - _Charles R Greathouse IV_, Aug 25 2017
%t LinearRecurrence[{1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1},{0,0,0,0,0,0,1,1,2,3,3,4,5,6,7,8,9,11,12,14,15,17,18,21,22,25,26},80] (* _Harvey P. Dale_, Nov 29 2017 *)
%o (PARI) Johnson(n,w,l)=my(pr=1); forstep(k=l,1,-1, pr=pr*(n-k)\(w-k)); pr\w
%o a(n)=Johnson(n,4,2) \\ _Charles R Greathouse IV_, Aug 25 2017
%o (PARI) a(n)=(n\2-1)*(n-1)\12 \\ _Charles R Greathouse IV_, Aug 25 2017
%o (Magma) [(n div 2-1)*(n-1) div 12: n in [1..80]]; // _Vincenzo Librandi_, Aug 26 2017
%K nonn,easy
%O 1,9
%A _N. J. A. Sloane_, Mar 13 2004
%E a(1)-a(6) and a(45)-a(57) from _Charles R Greathouse IV_, Aug 25 2017
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