cp's OEIS Frontend

A246175 The hyper-Wiener index of the Fibonacci cube Gamma(n) (n>=1).

%I A246175 #19 Nov 10 2024 14:40:49
%S A246175 1,5,23,89,325,1123,3750,12174,38682,120750,371478,1128810,3394159,
%T A246175 10112987,29892425,87737471,255912115,742272853,2142128604,6153811500,
%U A246175 17605105380,50174676300,142501128540,403422149220,1138714934125,3205372562369,8999834877995,25209180070037
%N A246175 The hyper-Wiener index of the Fibonacci cube Gamma(n) (n>=1).
%C A246175 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.
%H A246175 G. G. Cash, <a href="http://dx.doi.org/10.1016/S0893-9659(02)00059-9">Relationship between the Hosoya polynomial and the hyper-Wiener index</a>, Appl. Math. Letters, 15, 2002, 893-895.
%H A246175 S. Klavzar, M. Mollard, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match68/n1/match68n1_311-324.pdf">Wiener index and Hosoya polynomial of Fibonacci and Lucas cubes</a>, MATCH Commun. Math. Comput. Chem., 68, 2012, 311-324.
%H A246175 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6,-6,-19,24,24,-19,-6,6,-1).
%F A246175 G.f.: z*(1-z-z^2)/((1+z)^3*(1-3*z+z^2)^3).
%F A246175 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
%p A246175 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);
%t A246175 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 *)
%Y A246175 Cf. A246176
%K A246175 nonn,easy
%O A246175 1,2
%A A246175 _Emeric Deutsch_, Aug 18 2014