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%I #14 Dec 09 2017 19:26:28
%S 0,80,1552,27264,460544,7634944,125227008,2039840768,33069137920,
%T 534273589248,8610328346624,138508408717312,2225051277459456,
%U 35707816396193792,572608992614809600,9177150953877405696,147019299735681892352,2354527407788183781376
%N Harary index for the n-Keller graph.
%C The n-Keller graph is distance regular with 4^n vertices and for n > 1 the radius is 2. The degree of each vertex is 4^n - 3^n - n. - _Andrew Howroyd_, Dec 09 2017
%H Andrew Howroyd, <a href="/A296189/b296189.txt">Table of n, a(n) for n = 1..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (36, -432, 1984, -3072).
%F a(n) = 4^n*(4^n - (3^n + n + 1)/2)/2 for n > 1. - _Andrew Howroyd_, Dec 09 2017
%F a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4) for n > 5. - _Eric W. Weisstein_, Dec 09 2017
%F G.f.: -(16*x^2 (-5 + 83*x - 372*x^2 + 576*x^3)/((-1 + 4*x)^2*(1 - 28*x + 192*x^2))). - _Eric W. Weisstein_, Dec 09 2017
%t Table[If[n == 1, 0, 4^(n - 1) (2^(2 n + 1) - 3^n - n - 1)], {n, 20}]
%t Join[{0}, LinearRecurrence[{36, -432, 1984, -3072}, {80, 1552, 27264, 460544}, 20]]
%t CoefficientList[Series[-(16 x (-5 + 83 x - 372 x^2 + 576 x^3)/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x]
%o (PARI) a(n) = if(n>1, 4^n*(4^n - (3^n+n+1)/2)/2); \\ _Andrew Howroyd_, Dec 09 2017
%Y Cf. A292056.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Dec 07 2017
%E Terms a(8) and beyond from _Andrew Howroyd_, Dec 09 2017
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