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A246175 The hyper-Wiener index of the Fibonacci cube Gamma(n) (n>=1). 1
1, 5, 23, 89, 325, 1123, 3750, 12174, 38682, 120750, 371478, 1128810, 3394159, 10112987, 29892425, 87737471, 255912115, 742272853, 2142128604, 6153811500, 17605105380, 50174676300, 142501128540, 403422149220, 1138714934125, 3205372562369, 8999834877995, 25209180070037 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Fibonacci cube Gamma(n) can be defined as the graph whose vertices are the binary strings of length n without two consecutive 1's  and in which two vertices are adjacent when their Hamming distance is exactly 1.

LINKS

Table of n, a(n) for n=1..28.

G. G. Cash, Relationship between the Hosoya polynomial and the hyper-Wiener index, Appl. Math. Letters, 15, 2002, 893-895.

S. Klavzar, M. Mollard, Wiener index and Hosoya polynomial of Fibonacci and Lucas cubes, MATCH Commun. Math. Comput. Chem., 68, 2012, 311-324.

FORMULA

G.f.: z(1-z-z^2)/((1+z)^3*(1-3z+z^2)^3.

MAPLE

G := z*(1-z-z^2)/((1+z)^3*(1-3*z+z^2)^3): Gser := series(G, z = 0, 40): seq(coeff(Gser, z, j), j = 1 .. 35);

CROSSREFS

Cf. A246176

Sequence in context: A034447 A255803 A121329 * A283224 A178834 A255457

Adjacent sequences:  A246172 A246173 A246174 * A246176 A246177 A246178

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Aug 18 2014

STATUS

approved

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Last modified September 23 17:42 EDT 2017. Contains 292362 sequences.