A006186 Number of pair-coverings with largest block size 4. (Formerly M3773)

1, 5, 8, 10, 11, 12, 12, 13, 13, 13

Offset

4,2

Comments

The g.f. (1 + 5*z + 6*z^2 + z^3)/((z-1)*(z^2-z-1)) conjectured by Simon Plouffe in his 1992 dissertation is incorrect.

References

M. J. Grannell, T. S. Griggs, K. A. S. Quinn, R. G. Stanton, A census of minimum pair-coverings with restricted largest block length, Ars Combin., 52 (1999).

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

R. G. Stanton, J. L. Allston and D. D. Cowan, Pair-coverings with restricted largest block length, Ars Combin., 11 (1981), 85-98.

Links

Table of n, a(n) for n=4..13.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

R. G. Stanton, J. L. Allston and D. D. Cowan, Pair-coverings with restricted largest block length, Ars Combin., 11 (1981), 85-98. (Annotated scanned copy)

Crossrefs

Sequence in context: A276934 A127493 A331442 * A230457 A180748 A350377

Adjacent sequences: A006183 A006184 A006185 * A006187 A006188 A006189

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(13) from Grannell et al. added by Sean A. Irvine, Jan 18 2017

Status

approved