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A091848 Johnson bound J(n,4,2). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)