A000677 Number of bicentered trees with n nodes. (Formerly M2366 N0936)

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

0,7

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

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

Formula

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

Example

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

Maple

See link for Maple program.

Mathematica

See link.

Crossrefs

Cf. A000055, A000676.

Sequence in context: A295962 A097072 A049977 * A110865 A152982 A001642

Adjacent sequences: A000674 A000675 A000676 * A000678 A000679 A000680

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved