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%I #29 Oct 08 2023 04:44:40
%S 12,120,1008,1320,5460,4896,15960,12144,35100,24360,65472,42840,
%T 109668,68880,170280,103776,249900,148824,351120,205320,476532,274560,
%U 628728,357840,810300,456456,1023840,571704,1271940,704880,1557192,857280,1882188,1030200
%N a(n) = lcm(6n+2, 6n+4, 6n+6).
%H Colin Barker, <a href="/A061506/b061506.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F G.f.: (120*x^6 + 336*x^5 + 1500*x^4 + 840*x^3 + 960*x^2 + 120*x + 12)/((x-1)^4*(x+1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8), a(0)=12, a(1)=120, a(2)=1008, a(3)=1320, a(4)=5460, a(5)=4896, a(6)=15960, a(7)=12144. - _Harvey P. Dale_, Oct 22 2012
%F From _Colin Barker_, Mar 13 2017: (Start)
%F a(n) = 6*(3*n + 1)*(3*n + 2)*(n + 1) for n even.
%F a(n) = 3*(3*n + 1)*(3*n + 2)*(n + 1) for n odd.
%F (End)
%F From _Amiram Eldar_, Oct 08 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 11*sqrt(3)*Pi/144 - log(2)/6 - 3*log(3)/16.
%F Sum_{n>=0} (-1)^n/a(n) = log(3)/16 + log(2)/2 - Pi*sqrt(3)/16. (End)
%e lcm(2, 4, 6) = 12; lcm(8, 10, 12) = 120.
%t Table[LCM@@(6n+{2,4,6}),{n,0,40}] (* or *) LinearRecurrence[ {0,4,0,-6,0,4,0,-1},{12,120,1008,1320,5460,4896,15960,12144},40] (* _Harvey P. Dale_, Oct 22 2012 *)
%o (PARI) Vec(12*(1 + 10*x + 80*x^2 + 70*x^3 + 125*x^4 + 28*x^5 + 10*x^6) / ((1 - x)^4*(1 + x)^4) + O(x^50)) \\ _Colin Barker_, Mar 13 2017
%o (Magma) [Lcm([6*n+2, 6*n+4, 6*n+6]): n in [0..35]]; // _Vincenzo Librandi_, Mar 18 2018
%Y Cf. A005843.
%K easy,nonn
%O 0,1
%A _Jason Earls_, Jun 12 2001
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