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A284838 Number of edges in the n-Keller graph. 2

%I

%S 0,40,1088,21888,397312,6883328,116244480,1932230656,31778668544,

%T 518791888896,8424565768192,136279337467904,2198302774788096,

%U 35386835907641344,568757233463066624,9130929873047519232,146464646890277306368,2347871574175904694272

%N Number of edges in the n-Keller graph.

%H Colin Barker, <a href="/A284838/b284838.txt">Table of n, a(n) for n = 1..800</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) = 2^(2*n-1)*(4^n-3^n-n).

%F From _Robert Israel_, Apr 04 2017: (Start)

%F G.f.: 8*(5-44*x)*x^2/((1-16*x)*(1-12*x)*(1-4*x)^2).

%F E.g.f.: exp(16*x)/2-exp(12*x)/2-2*x*exp(4*x).

%F (End)

%F a(n) = 36*a(n-1) - 432*a(n-2) + 1984*a(n-3) - 3072*a(n-4) for n>4. - _Colin Barker_, Apr 04 2017

%p f:= n -> 2^(2*n-1)*(4^n-3^n-n):

%p map(f, [$1..30]); # _Robert Israel_, Apr 04 2017

%t Table[2^(2 n - 1) (4^n - 3^n - n), {n, 15}]

%t LinearRecurrence[{36, -432, 1984, -3072}, {0, 40, 1088, 21888}, 20] (* _Eric W. Weisstein_, Mar 21 2018 *)

%t CoefficientList[Series[-((8 x (-5 + 44 x))/((1 - 4 x)^2 (1 - 28 x + 192 x^2))), {x, 0, 20}], x] (* _Eric W. Weisstein_, Mar 21 2018 *)

%o (PARI) concat(0, Vec(8*(5-44*x)*x^2/((1-16*x)*(1-12*x)*(1-4*x)^2) + O(x^30))) \\ _Colin Barker_, Apr 04 2017

%o (Python) def a(n): return 2**(2*n-1)*(4**n-3**n-n) # _Indranil Ghosh_, Apr 04 2017

%Y Cf. A000302(n) = 4^n (number of vertices in the n-Keller graph).

%Y Cf. A284850(n) = a(n)/2^(2*n-1) (vertex degrees of the n-Keller graph).

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Apr 03 2017

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Last modified April 3 13:32 EDT 2020. Contains 333197 sequences. (Running on oeis4.)