Cats & Alligators has just made it into Neil Sloane's "On-Line Encyclopedia of Integer Sequences"! Here's how the top of A001037 now reads: ID Number: A001037 (Formerly M0116 and N0046) URL: http://www.research.att.com/projects/OEIS?Anum=A001037 Sequence: 1,2,1,2,3,6,9,18,30,56,99,186,335,630,1161,2182,4080,7710, 14532,27594,52377,99858,190557,364722,698870,1342176, 2580795,4971008,9586395,18512790,35790267,69273666, 134215680,260300986,505286415,981706806 Name: Degree n irreducible polynomials over GF(2); n-bead necklaces with beads of 2 colors when turning over is not allowed and with primitive period n; binary Lyndon words of length n. Comments: Also dimensions of free Lie algebras - see A059966, which is essentially the same sequence. References E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84. R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. P. J. Freyd and A. Scedrov, Categories, Allegories, North-Holland, Amsterdam, 1990. See 1.925. E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois J. Math., 5 (1961), 657-665. M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964) 285-299. M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 79. G. Melancon, Factorizing infinite words using Maple, MapleTech journal, vol 4, no. 1, 1997, pp. 34-42, esp. p. 36. M. R. Nester, (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. G. Viennot, Algebres de Lie Libres et Monoides Libres, Lecture Notes in Mathematics 691, Springer verlag 1978. Postscript^3: For the record, this is the 8th item in which my name appears. The complete list: A000602 A000628 A000670 A001037 A067608 A067609 A067610 A067765