The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. Index entries for linear recurrences with constant coefficients, signature (6, -6, -19, 24, 24, -19, -6, 6, -1). FORMULA G.f.: z(1-z-z^2)/((1+z)^3*(1-3z+z^2)^3. 625*a(n) = -1/2*(-1)^n*(74+45*n+5*n^2) -5*(2*A001871(n)-3*A001871(n-1)) +17*A001906(n)-53*A001906(n+1) +50*(2*A246178(n)-3*A246178(n-1)) . - R. J. Mathar, Jul 22 2022 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); MATHEMATICA CoefficientList[Series[z (1-z-z^2)/((1+z)^3(1-3z+z^2)^3), {z, 0, 30}], z] (* Harvey P. Dale, Mar 05 2019 *) CROSSREFS Cf. A246176 Sequence in context: A034447 A255803 A121329 * A362764 A283224 A178834 Adjacent sequences: A246172 A246173 A246174 * A246176 A246177 A246178 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Aug 18 2014 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.

Last modified August 4 07:10 EDT 2024. Contains 374905 sequences. (Running on oeis4.)