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A192858 Hosoya indices of the 2n-wheel graphs W_{2n}.

%I A192858 #35 Feb 16 2025 08:33:15
%S A192858 2,10,36,120,382,1178,3550,10514,30720,88788,254342,723190,2043386,
%T A192858 5742490,16062492,44744688,124192270,343594514,947857750,2608015778,
%U A192858 7159034232,19609583820,53608363286,146290947310,398552156402,1084153113898,2944982283540,7989231439464,21646950044830,58585895022218,158389325993422
%N A192858 Hosoya indices of the 2n-wheel graphs W_{2n}.
%C A192858 Wheel graphs are defined for n >= 4; extended to n=2 using recurrence.
%C A192858 Binomial transform of A120940 multiplied by 2. - _R. J. Mathar_, Jul 11 2011
%H A192858 Vincenzo Librandi, <a href="/A192858/b192858.txt">Table of n, a(n) for n = 1..200</a>
%H A192858 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HosoyaIndex.html">Hosoya Index</a>
%H A192858 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WheelGraph.html">Wheel Graph</a>
%H A192858 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1)
%F A192858 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).
%F A192858 G.f.: 2*x*(1+x)*(x-1)^2 / ( (x^2 - 3*x + 1)^2 ). - _R. J. Mathar_, Jul 11 2011
%F A192858 a(n) = ((3+r)^n*((5-r)*n+3*r-5) + (3-r)^n*((5+r)*n-3*r-5))/(5*2^n) with r=sqrt(5). - _Bruno Berselli_, Aug 31 2011
%F A192858 a(n) = 2*A377857(n+2). - _R. J. Mathar_, Dec 16 2024
%t A192858 LinearRecurrence[{6, -11, 6, -1}, {10, 36, 120, 382}, {0, 30}]
%o A192858 (Magma) I:=[2,10,36,120]; [n le 4 select I[n] else 6*Self(n-1)-11*Self(n-2)+6*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Aug 31 2011
%o A192858 (PARI) x='x+O('x^30); Vec(2*x*(1+x)*(x-1)^2/((x^2-3*x+1)^2)) \\ _G. C. Greubel_, Nov 10 2018
%K A192858 nonn,easy
%O A192858 1,1
%A A192858 _Eric W. Weisstein_, Jul 11 2011