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%I #18 Sep 08 2022 08:46:00
%S 0,1,9,61,385,2365,14353,86605,521089,3130909,18798577,112830829,
%T 677103073,4062972733,24378899281,146276584333,877669071937,
%U 5266043129437,31596344870065,189578327500717,1137470739845281,6824826763594621,40948967555136529
%N Eccentricity of Tower of Hanoi graph H_n^{3} (divided by 3).
%H Andreas M. Hinz and Daniele Parisse, <a href="http://dx.doi.org/10.1007/s00373-011-1076-4">The Average Eccentricity of Sierpinski Graphs</a>, Graphs and Combinatorics, 2011.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,18).
%F y(0)=0; y(n+1) = 6*y(n) + 2*3^n + 3 - 2*0^n. a(n)=y(n)/3.
%F a(n) = -2*3^(n-2) +14*6^n/45-1/5, n>0. - _R. J. Mathar_, Dec 13 2011
%F G.f.: x*(1+x)*(2*x-1) / ( (x-1)*(6*x-1)*(3*x-1) ). - _R. J. Mathar_, Dec 13 2011
%t Join[{0}, LinearRecurrence[{10, -27, 18}, {1, 9, 61}, 25]] (* _Vincenzo Librandi_, Sep 11 2015 *)
%o (PARI) Vec(x*(1+x)*(2*x-1) / ( (x-1)*(6*x-1)*(3*x-1) ) + O(x^40)) \\ _Michel Marcus_, Sep 11 2015
%o (Magma) [0] cat [-2*3^(n-2) +14*6^n/45-1/5: n in [1..25]]; // _Vincenzo Librandi_, Sep 11 2015
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 20 2011
%E a(21)-a(22) from _Vincenzo Librandi_, Sep 11 2015
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