A091848 Johnson bound J(n,4,2).

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, 30, 33, 35, 38, 40, 44, 45, 49, 51, 55, 57, 61, 63, 68, 70, 75, 77, 82, 84, 90, 92, 98, 100, 106, 108, 114, 117, 123, 126, 133, 135, 142, 145, 152, 155, 162, 165

Offset

1,9

Comments

A quasipolynomial of order 24 and degree 2. - Charles R Greathouse IV, Aug 25 2017

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 527, Cor. 5.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

W. Chu and C. J. Colbourn, Optimal (n,4,2)-OCC of small orders, Discrete Math., 279 (2004), 163-172.

Wikipedia, Johnson bound

Index entries for linear recurrences with constant coefficients, 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).

Formula

a(n) = n^2/24 - O(n). - Charles R Greathouse IV, Aug 25 2017

Mathematica

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 *)

Prog

(PARI) Johnson(n, w, l)=my(pr=1); forstep(k=l, 1, -1, pr=pr*(n-k)\(w-k)); pr\w
a(n)=Johnson(n, 4, 2) \\ Charles R Greathouse IV, Aug 25 2017
(PARI) a(n)=(n\2-1)*(n-1)\12 \\ Charles R Greathouse IV, Aug 25 2017
(Magma) [(n div 2-1)*(n-1) div 12: n in [1..80]]; // Vincenzo Librandi, Aug 26 2017

Crossrefs

Sequence in context: A034886 A011882 A025767 * A017886 A029038 A011877

Adjacent sequences: A091845 A091846 A091847 * A091849 A091850 A091851

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 13 2004

Extensions

a(1)-a(6) and a(45)-a(57) from Charles R Greathouse IV, Aug 25 2017

Status

approved