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A067046 a(n) = lcm(n, n+1, n+2)/6.

%I A067046 #49 Dec 04 2024 16:49:32
%S A067046 1,2,10,10,35,28,84,60,165,110,286,182,455,280,680,408,969,570,1330,
%T A067046 770,1771,1012,2300,1300,2925,1638,3654,2030,4495,2480,5456,2992,6545,
%U A067046 3570,7770,4218,9139,4940,10660,5740,12341,6622,14190,7590,16215,8648,18424,9800
%N A067046 a(n) = lcm(n, n+1, n+2)/6.
%H A067046 Harry J. Smith, <a href="/A067046/b067046.txt">Table of n, a(n) for n = 1..1000</a>
%H A067046 Amarnath Murthy, <a href="http://fs.unm.edu/SN/SomeNotionsLeast.pdf">Some Notions on Least Common Multiples</a>, Smarandache Notions Journal, Vol. 12, No. 1-2-3 (Spring 2001), pp. 307-308.
%H A067046 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%H A067046 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%F A067046 G.f.: (x^4 + 2x^3 + 6x^2 + 2x + 1)/(1 - x^2)^4.
%F A067046 a(n) = binomial(n+2,3)*(3-(-1)^n)/4. - _Gary Detlefs_, Apr 13 2011
%F A067046 Quasipolynomial: a(n) = n(n+1)(n+2)/6 when n is odd and n(n+1)(n+2)/12 otherwise. - _Charles R Greathouse IV_, Feb 27 2012
%F A067046 a(n) = A033931(n) / 6. - _Reinhard Zumkeller_, Jul 04 2012
%F A067046 From _Amiram Eldar_, Sep 29 2022: (Start)
%F A067046 Sum_{n>=1} 1/a(n) = 6*(1 - log(2)).
%F A067046 Sum_{n>=1} (-1)^(n+1)/a(n) = 6*(3*log(2) - 2). (End)
%e A067046 a(6) = 28 as lcm(6,7,8)/6 = 168/6 = 28.
%t A067046 Table[LCM[n,n+1,n+2]/6,{n,50}] (* _Harvey P. Dale_, Jan 11 2011 *)
%o A067046 (PARI) a(n)={lcm([n, n+1, n+2])/6} \\ _Harry J. Smith_, Apr 30 2010
%o A067046 (PARI) a(n)=binomial(n+2,3)/(2-n%2) \\ _Charles R Greathouse IV_, Feb 27 2012
%o A067046 (Haskell)
%o A067046 a067046 = (`div` 6) . a033931  -- _Reinhard Zumkeller_, Jul 04 2012
%Y A067046 Cf. A000447 (bisection), A006331 (bisection), A033931.
%K A067046 nonn,easy
%O A067046 1,2
%A A067046 _Amarnath Murthy_, Dec 30 2001