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%I #13 Dec 07 2017 22:14:28
%S 0,1,15,75,162,1317,2610,20505,40212,315957,622350,4917585,9739512,
%T 77326797,153754290,1224577065,2440906812,19477524837,38880209430,
%U 310591650945,620507282112,4959998206077,9913902403770,79274639451225,158494393505412,1267625772746517
%N Numerators of Harary index for the n-Mycielski graph.
%C Denominators are 1, 1, 2, followed by 2, 1, 2, 1, ....
%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/MycielskiGraph.html">Mycielski Graph</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 30, 0, -273, 0, 820, 0, -576).
%F a(n) = ((3 + (-1)^n)*(432 - 135*2^(n + 2) + 112*3^n + 81*4^n))/1152 for n > 3.
%F a(n) = 30*a(n-2) - 273*a(n-4) + 820*a(n-6) - 576*a(n-8) for n > 11.
%F G.f.: x^2*(1 + 15*x + 45*x^2 - 288*x^3 - 660*x^4 + 1845*x^5 + 650*x^6 -
%F 6162*x^7 - 576*x^8 + 4320*x^9)/(1 - 30*x^2 + 273*x^4 - 820*x^6 +
%F 576*x^8).
%e 0, 1, 15/2, 75/2, 162, 1317/2, 2610, 20505/2, 40212, ...
%t Table[If[n == 1, 0, 3/4 - 15 2^(-4 + n) + (7 3^(-2 + n))/4 + 9 4^(-3 + n)], {n, 30}] // Numerator
%t Join[{0, 1, 15}, Table[((3 + (-1)^n) (432 - 135 2^(n + 2) + 112 3^n + 81 4^n))/1152, {n, 4, 20}]]
%t Join[{0, 1, 15}, LinearRecurrence[{0, 30, 0, -273, 0, 820, 0, -576}, {75, 162, 1317, 2610, 20505, 40212, 315957, 622350}, 20]]
%t CoefficientList[Series[x (1 + 15 x + 45 x^2 - 288 x^3 - 660 x^4 + 1845 x^5 + 650 x^6 - 6162 x^7 - 576 x^8 + 4320 x^9)/(1 - 30 x^2 + 273 x^4 - 820 x^6 + 576 x^8), {x, 0, 20}], x]
%o (PARI) first(n) = Vec(x^2*(1 + 15*x + 45*x^2 - 288*x^3 - 660*x^4 + 1845*x^5 + 650*x^6 - 6162*x^7 - 576*x^8 + 4320*x^9)/(1 - 30*x^2 + 273*x^4 - 820*x^6 + 576*x^8) + O(x^(n+1)), -n) \\ _Iain Fox_, Dec 07 2017
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Dec 07 2017
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