A000677 Number of bicentered trees with n nodes.

0, 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108, 267, 619, 1541, 3762, 9497, 23907, 61216, 157211, 407919, 1063398, 2792026, 7365532, 19535887, 52037837, 139213244, 373820978, 1007420841, 2723783122, 7387129661, 20091790330, 54793762295, 149808274055, 410553630946

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

See A000676 for more information.

On the bottom of first page 266 of article Cayley (1881) is a table of A000676 and A000677 for n = 1..13. - Michael Somos, Aug 20 2018

Examples

			G.f. = x^2 + x^4 + x^5 + 3*x^6 + 4*x^7 + 11*x^8 + 20*x^9 + 51*x^10 + ... - _Michael Somos_, Aug 20 2018
		

References

• N. L. Biggs et al., Graph Theory 1736-1936, Oxford, 1976, p. 49.
• A. Cayley, On the analytical forms called trees, with application to the theory of chemical combinations, Reports British Assoc. Advance. Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 438).
• 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

• Geoffrey Critzer, Table of n, a(n) for n = 0..200 (replacing the first version from N. J. A. Sloane)
• Jean-François Alcover, Mathematica program
• A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 266-268.
• E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees)., J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
• J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
• N. J. A. Sloane, Maple program
• Eric Weisstein's World of Mathematics, Bicentered Tree.
• Index entries for sequences related to trees

Crossrefs

Cf. A000055, A000676.

Programs

Maple

# See link for Maple program.

Mathematica

(* See link. *)

Formula

a(n) = A000055(n) - A000676(n).