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%I #17 Sep 02 2022 20:34:21
%S 12,200,2944,43392,650240,9889792,152174592,2362671104,36940546048,
%T 580718690304,9167616081920,145195622465536,2305296785473536,
%U 36670757861851136,584164270070038528,9315814196367065088,148683258271895650304,2374494908625021042688
%N Wiener index of the n-Keller graph.
%C The Keller graph is connected for n >= 2.
%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. Sequence extrapolated to n = 1 using formula. (The Keller graph is disconnected for n = 1, so a(1) is not the Wiener index of that graph.) - _Andrew Howroyd_, Sep 08 2017
%H Andrew Howroyd, <a href="/A292056/b292056.txt">Table of n, a(n) for n = 1..100</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WienerIndex.html">Wiener Index</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 - 2) / 2. - _Andrew Howroyd_, Sep 08 2017
%F a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4).
%F G.f.: -((8 x (-25 + 532 x - 2976 x^2 + 4608 x^3))/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))).
%F E.g.f.: exp(4*x)*(exp(8*x) + exp(12*x) + 4*x - 2)/2. - _Stefano Spezia_, Sep 02 2022
%t Table[4^n (4^n + 3^n + n - 2)/2, {n, 20}]
%t LinearRecurrence[{36, -432, 1984, -3072}, {12, 200, 2944, 43392}, 20]
%t CoefficientList[Series[-((8 (-25 + 532 x - 2976 x^2 + 4608 x^3))/((-1 + 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x]
%o (PARI) a(n) = 4^n * (4^n + 3^n + n - 2) / 2; \\ _Andrew Howroyd_, Sep 08 2017
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Sep 08 2017
%E Terms a(7) and beyond from _Andrew Howroyd_, Sep 08 2017
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