%I #15 Feb 16 2025 08:33:53
%S 0,10,29,84,247,734,2193,6568,19691,59058,177157,531452,1594335,
%T 4782982,14348921,43046736,129140179,387420506,1162261485,3486784420,
%U 10460353223,31381059630,94143178849,282429536504,847288609467,2541865828354,7625597485013
%N Number of vertices at distance 2 from a given vertex in the n-Keller graph.
%C The radius of the n-Keller graph is 2 for n > 1. - _Andrew Howroyd_, Mar 23 2018
%H Colin Barker, <a href="/A301571/b301571.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphDistance.html">Graph Distance</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).
%F a(n) = 3^n + n - 1 for n > 1. - _Andrew Howroyd_, Mar 23 2018
%F From _Colin Barker_, Mar 24 2018: (Start)
%F G.f.: x^2*(5 - 3*x)*(2 - 3*x) / ((1 - x)^2*(1 - 3*x)).
%F a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3) for n>4.
%F (End)
%o (PARI) concat(0, Vec(x^2*(5 - 3*x)*(2 - 3*x) / ((1 - x)^2*(1 - 3*x)) + O(x^60))) \\ _Colin Barker_, Mar 24 2018
%Y Cf. A284850 (number of vertices at distance 1 = vertex degree), A292056.
%K nonn,easy,changed
%O 1,2
%A _Eric W. Weisstein_, Mar 23 2018