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Expansion of 36*x^2*(1+6*x-36*x^2) / ( (1-6*x)^2 *(1+6*x+36*x^2) ).
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%I #19 Jul 04 2019 10:47:53

%S 0,36,432,1296,15552,139968,559872,5038848,40310784,181398528,

%T 1451188224,10883911680,52242776064,391820820480,2821109907456,

%U 14105549537280,101559956668416,710919696678912,3656158440062976,25593109080440832,175495605123022848,921351926895869952

%N Expansion of 36*x^2*(1+6*x-36*x^2) / ( (1-6*x)^2 *(1+6*x+36*x^2) ).

%C The old definition was: Colorless combinations of quarks and antiquarks of length n >= 1.

%D Florentin Smarandache, "Matter, Antimatter and Unmatter", Infinite Energy, Concord, NH, USA, Vol. 11, Issue 62, 50-51, 2005.

%H Florentin Smarandache, <a href="http://cdsweb.cern.ch/record/798551/files/ext-2004-142.pdf?version=1">A New Form of Matter - Unmatter, Formed by Particles and Anti-Particles"</a>, EXT-2004-182 in CERN's web site, 2004.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,216,-1296).

%F a(n) = ( n - 1 - 2*floor((n-1)/3) )*6^n.

%t Table[(n - 1 - 2 Floor[(n - 1)/3]) 6^n, {n, 1, 30}]

%t LinearRecurrence[{6,0,216,-1296},{0,36,432,1296},30] (* _Harvey P. Dale_, Jul 04 2019 *)

%o (PARI) concat(0, 36*Vec(x*(1+6*x-36*x^2) / (1-6*x)^2 / (1+6*x+36*x^2)+O(x^99)))

%K nonn,easy

%O 1,2

%A Florentin Smarandache (smarand(AT)unm.edu), Nov 04 2010

%E Entry revised by Editors of the OEIS, Sep 11 2014