The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221042 The Wiener index of the Bethe cactus lattice graph D_n defined pictorially in the Hosoya - Balasubramanian reference. 1
8, 212, 3632, 50504, 624632, 7190492, 78973664, 839594768, 8717571176, 88915009892, 894366753296, 8896551656792, 87694439633240, 857879937077612, 8338591552929728, 80606380453484576, 775488956137204424, 7429684469671844852, 70919715248730034160, 674750433200813750120 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
K. Balasubramanian, Recent developments in tree-pruning methods and polynomials for cactus graphs and trees, J. Math. Chemistry, 4 (1990) 89-102.
H. Hosoya, K. Balasubramanian, Exact dimer statistics and characteristic polynomials of cacti lattices, Theor. Chim. Acta 76 (1989) 315-329.
LINKS
FORMULA
a(n) = (1/2)+3^n*(3*n+4)+3^(2*n)*(3*n-9/2).
G.f.: 4*x*(2+3*x+27*x^2)/((1-x)*(1-3*x)^2*(1-9*x)^2). - Bruno Berselli, Dec 30 2012
MAPLE
a := proc (n) options operator, arrow: 1/2+3^n*(3*n+4)+3^(2*n)*(3*n-9/2) end proc: seq(a(n), n = 1 .. 20);
CROSSREFS
Cf. A221043.
Sequence in context: A197767 A024288 A081794 * A358211 A247032 A027646
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Dec 30 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 18:59 EDT 2024. Contains 372765 sequences. (Running on oeis4.)