A004037 The coding-theoretic function A(n,6,4). (Formerly M0291 N0104)

1, 1, 1, 2, 2, 3, 5, 6, 9, 13, 14, 15, 20, 20, 22, 25, 30, 31, 37, 40, 42, 50, 52, 54, 63, 65, 67, 76, 80, 82, 92, 96, 99, 111, 114, 117, 130, 133, 136, 149, 154, 157, 171, 176, 180, 196, 200, 204, 221, 225, 229, 246, 252, 256, 274, 280, 285, 305, 310, 315, 336

Offset

4,4

Comments

Packing number D(n,4,2). Maximum number of edge-disjoint K_4's in a K_n. - Rob Pratt, Feb 26 2024

References

CRC Handbook of Combinatorial Designs, 1996, p. 411.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=4..64.

A. E. Brouwer, Bounds for binary constant weight codes

A. E. Brouwer, Optimal packings of K_4's into a K_n, J. Combin. Theory, A 26 (1979), 278-297.

A. E. Brouwer, A. Schrijver, and H. Hanani, Group divisible designs with block-size four, Discrete Math. 20 (1977/78), no. 1, 1-10.

A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, New table of constant weight codes, IEEE Trans. Info. Theory 36 (1990), 1334-1380.

Richard K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Department of Mathematics, University of Calgary, January 1967. [Annotated and scanned copy, with permission]

Sascha Kurz, Plane point sets with many squares or isosceles right triangles, arXiv:2112.12716 [math.CO], 2021.

Alice Miller and Michael Codish, Graphs with girth at least 5 with orders between 20 and 32, arXiv:1708.06576 [math.CO], 2017, Table 3.

Index entries for sequences related to A(n,d,w)

Crossrefs

Sequence in context: A335755 A325338 A143438 * A291296 A292906 A160235

Adjacent sequences: A004034 A004035 A004036 * A004038 A004039 A004040

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset corrected by Zhao Hui Du, Aug 14 2008

Offset 4 and a(4) inserted by Jeremy Tan, Feb 16 2022

a(56)-a(64) from Rob Pratt, Feb 27 2024

Status

approved